:::Shrug::: your car, your tire, your life.
Several years ago there was a case inSan Diego a tire that had been improperly repaired two years prior failed, the van flipped over and two people died. There was an 8 million dollar judgement against the dealership AND the guy that did the repair.
What once was considered an OK repair for a tire with a 10,000 mile service life is not considered a proper repair for a tire with a 80,000 mile service life.
Some car makers have gone to the point that they say no repair is acceptable.
I don’t know if this http://www.tirereview.com/22-8-million-faulty-tire-repair-entirely-avoidable/ is the incident to which you refer, but it seems that they only put a patch on and not a plug.
"The puncture was “repaired” using only a patch – no plug of any kind was installed – and the damaged area was in no way prepared – the puncture was not reamed out and the innerliner was not cleaned or scraped – to accept the repair, again contrary to advised industry practice. Further, no sealant was used to cover the patch.
The important thing about items like “Fix a Flat” is that they can help get the stranded car off the road and the person to their destination. Then get the tire looked at by an expert to see if it can be properly repaired. Building a relationship with a particular dealer/repair garage can get you honest answers that will save money and/or save the car from accidents.
Just a suggestion … but why not carry a properly inflated spare tire , and replace the wheel when you have a puncture. A lot easier than trying to fix a puncture in situ, shirley …
Some cars these days (like mine) come without a spare, just a Fix-a-Flat and pump.
One piece patch and plugs are fine for small punctures. Temporary plugs are supposed to be temporary.
I once got a crescent wrench in a tire. That was a hole.
As a pedestrian, I’ve often noticed how any bit of debris in the right part of the road will tend to dance and skip as successive cars drive over it. Even things that naturally lie flat will eventually find themselves tumbling - and if your wheel catches them at the right (wrong) bit of a mid-tumble caused by the car in front, the thing is going in your tyre.
It’s a statistical thing - like landing a coin on its edge - unlikely events start to happen after enough tries.
Stop calling me Shirley. 
As others mentioned, some cars don’t come with spares and carrying one can take up too much space, or you can be too broke to have a good one but need a car for job interviews. The list can be long.
But having a proper spare and the tools and know-how to switch tires is the safest bet for sure.
When I worked in a service station, the only plugs we had were like these and were for big holes. They had to go on from the inside like a regular patch. We very rarely ever used them, mostly we just patched the tires and let it go. Or, if it were a special case (hole too big, multiple patches, etc.), we patched it and put in a tube.
And Fix-a-Flat should be outlawed. That crap is the devil’s cum. It’s wicked nasty shit and I hated fixing tires that had it in there, especially when some idiot tried it and naturally it didn’t work (just like I told him it wouldn’t) and then he wanted the tire patched. Then he was stupid enough to wonder why it took so long. Because I had to spend half an hour wiping out all that crap I told you wouldn’t work just so I could actually fix the damn tire idiot!
When I got the screw in my motorcycle sidewall, the dealer said that plugs and patches might work for the tread - but a sidewall does a lot more flexing, and a patch likely would not last long on that. They wouldn’t even try to repair it.
md2000, what your dealer told you is correct, especially on motorcycles and “special use/racing tires”. He was right to replace, not repair IMO.
If it was the same wheel, then either someone’s screwing with you, or you need to take better care where you’re driving.
If it was a different wheel, it’s possible you got both at the same place, running over a bunch of spilled screws.
How likely is it that someone knelt by your car with a power screwdriver and a screw? Twice? I doubt it. My guess is there are easier ways to mess with you.