OK, maybe the OP should have started with “what should my budget be?”. I can go higher, as I said, to get the right thing. I’d like to keep it below 1K if possible.
Canon 550d or Nikon D5100 would be my vote then, but it does matter what her preferences are, as far as size and handling goes.
Its a bit Pepsi vs Coke, no real difference but can bug the heck out of you if your preference is for one.
At this point it’s just anecdotal. Until I see some real data I would attribute this to random noise. All cameras have some amount of problems like this (like the notorious Canon E99 problem, which also didn’t really exist). But they most often turn out to be nothing real in terms of statistical analysis. Based on the number of people I personally know with that camera I would discount the problem.
Nikon and Canon get a lot of looks from people fr two reasons. Name recognition. They’re great cameras. But, a serious shopper may also want to look at the Sony dSLRs (which is what the Minolta and Konica/Minolta morphed into) and the Pentax dSLRs. For entry level cameras and price points with kit lenses, you really can hardly make a bad choice here. The Micro4/3rds and the 4/3rds mentioned from Panasonic and Olympus can also be included.
When I use to sell 35mm SLRs in the early 80s, we had all the same questions. Which brand? Which model? And I use to tell them all this: the photographer makes the photo. Get a major brand and you’ll likely have a tool of sufficient quality for your use.
ymmv
Its not only about name recognition in my view.
In my view its generally a lot easier to go with the big two, particularly for beginners - more camera specific info, more tutorials based on those models, more lenses made for those companies etc etc.
If there was some big advantage in going for a non-Canikon brand that would be one thing, but generally there isnt.
Otara
Did you notice I listed two reasons?
Yeah, Canon and Nikon get the most attention in a lot of areas. I have used both brands professionally, and I am currently teaching digital photography, both basics and advanced techniques. When someone in person asks me these questions, I feel them out, find out what they’re into, what level they are or want to be at, even take them shopping so they can try things hands on. And yes, most choose either a Canon or a Nikon. I’m just always happy to point out that there are other options. And for some people, the best choice for them might not be either of the big two.
My current cameras are Nikons, and I’m rather stuck financially in staying within this brand. Lots of my students choose Canon, I think primarily for the “feel” of the cameras. The Canon entry level dSLRs are very user friendly.
This is the big thing, as I mentioned in my initial post. Camera choice can be (or is) very personal. When NoClueBoy says a lot of his students find Canons more intuitive and feel better, I feel exactly the opposite. Canon controls frustrate me and I prefer the way Nikons feel in my hands (although this is based mostly on my experienced with the pro-level cameras.) There’s really no substitute to getting these cameras in your hands and playing around with them.
I’ve been using a Pentax K100D steady since 2006. It’s a sturdy piece (even accidently dropped it on a granite rock from chest height.) with a good range of lenses. Apparently the newer models are just as good, especially on the mid to low end range of the dSLR catalog. It’s not as quiet or as light as my dad’s Nikon D80, but he’s always a bit jealous of the picture quality I seem to get out of the Pentax.
Can you use her old lenses on the new camera? Does she have lenses that she would want to use again?
“Did you notice I listed two reasons?”
I did but really you nullified the second by subsequently saying they’re basically as good as other brands in practise.
My point was similar to yours in that camera quality only matters to a certain point, but there were other significant reasons why its good to be cautious about going outside the two major brands that you had not mentioned.
Otara
The D90 is still in contention, and at the top of the list. Not quite ready to get one yet, but I’m hoping to this year or next.
I have entirely too many cameras, and they are different brands. Nikon FM2 and FM3a, Olympus OM-1N and OM-4, Canon AE-1 Program, and a Pentax K-1000. Not to mention the rest. All I need is to look at another brand with a different lens system! 
No, unfortunately. It’s been a while.
Basically any DSLR will be sufficient for the average skilled photographer. I browse Wikipedia frequently just looking at photos, and I always check the camera data on the photo page to see what model of camera and what exposure settings were used. It is plainly obvious that excellent quality photographs can be gotten with every DSLR under the sun, from the earliest Nikon D1 models to the entry level models to the latest, most expensive and feature-packed models. The basic principles of SLR photography are unchanged since the days of film. $500 is by no means a “really low” budget.
A skilled photographer can take a basic used Nikon D40 with a 50mm fixed lens, the whole package costing around four hundred dollars, and if he is sufficiently good at composition and exposure, he can start taking professional level pictures that can earn him money. A bad or mediocre photographer can get the most expensive camera and lenses on the planet and it won’t amount to anything.
The most important thing is getting a camera that feels right to you. Most of it is simple ergonomics. It varies from person to person.
I have never had a problem with my D90. I own seven cameras, and since I got my D90, the others are collecting dust.
If your budget is forcing you to buy a 8 year old used camera and one lens, then yeah, it is a low budget.
As always, YMMV. 
What is vitally important to some won’t even be a minor point to others. And if one is going to stick to a basic package and probably not much else after the initial purchase (which many, many people end up doing), then there are almost too many options to consider. One does need to begin paring down a list somehow, and if brand power comes across as really important to the person, I see no problem in that.
What I’m wondering now is, does the OP feel helped by all our input?
Just for fun, we should look at the last couple of threads like this that we’ve been involved in and see what specific models are still current, or even if they’re still on the market at all.
I don’t think that’s what Our Man In The Tall, Slender Silver Structure was getting at. I think his point is that making good pictures depends, within certain limits, on the skill of the photographer more than the cost of the equipment.
Absolutely. However, there are some pretty tangible differences between old and new dSLR technology that I think are readily accessible to the beginning photographer, most specifically, high-ISO performance.
Another great site for comparisons is http://www.dxomark.com/, but that’s a little bit more technical, and you need to know what you’re looking at.
Comparing various cameras at that site, I personally would think the Nikon D5100 would be my choice now for entry-level dSLR, although I would have to work with it myself to see. Just going by the numbers, it seems to be a better choice than the D90, too. But numbers are one thing, and real-world results can be different. Honestly, I really don’t see any reason to choose the D90 over the D5100 (this is for Johnny L.A.) Plus it’s about $250 cheaper. ETA: The biggest differences are the D90 has a built-in focus motor (so your AF screw-focus lenses will focus, which is actually a somewhat important consideration. For example, I have an 85mm f/1.4 that wouldn’t AF on the D5100, and is a beast of a portrait lens.) Also the D90 achieves a 4.5 FPS rate vs the 4.0 FPS of the D5100, which I don’t think is too big of a difference.
ETA2: Here’s another comparison of those two cameras.