I can verify that. I’ve been to a restaurant where they do that, and I asked why, and this is exactly what they told me.
Though I would argue it’s not just the customers: I don’t know how many times my dad has ordered his usual medium well, which should have a slight kiss (or stripe) of pink in it, and instead got a hockey puck.
Yes, but it’s not the same throughout the steak.
As I understand it, blue rare is all red except the outside. Rare still has a lot of red. Medium rare has a bit of red. Medium has pink but no red. Medium-well is mostly brown but with a bit of pink, and well is brown all the way through.
So, if someone told me the choices were “mostly pink, a little pink, or no pink,” I would assume that medium (or perhaps medium-rare) was the minimum.
That said, none of it is spectral red, so I could see some people considering what I call red to be a dark pink.
I know that*; but people who know use ‘bloody’ colloquially, and many people don’t know just think it’s blood. And ‘Bloody, but not cold’ is easier to say than ‘Plenty of myoglobin, but not cold’. 
*I actually learned that here several years ago, when I asked about a kosher rule.
That will actually attract some people. Hot sauces so spicy they require a waiver are a big draw. Fugu (blowfish) is potentially deadly yet it’s an expensive delicacy, probably in part because people eating it are risking so much.
Aside from the euphoria of risk-taking, people also feel “elite” for eating something the average person is too scared to eat.
Your conclusion is correct, but a correction, or refinement, on your premise of “difficult in a restaurant.” Restarants have long used sous-vide, way before you or I ever heard of it (:)), precisely because you “can’t predict your orders in advance.”
Your premise here and in your earlier post recognizing the management of restaurant kitchens is exactly on point*. With it meat dishes (although possible, inadvisable due to breakdown of the flesh over time with fish or vegetables) can be precooked and held safely at any temperature (lowest with steaks to allow up-firing), which simplifies a lot of things.
Unintended little pun on à point* here, but FTR it introduces a word and term novel to us benighted steak-doneness parsers.
If you grind it yourself, or have a butcher do so, it is a lot safer. See, ground beef chubs, etc, will/can contain meat from a large number of cattle.
Beef chubs: the fabled surf-and-turf all-in-one animal.
Seriously, though, the fact of the hodge-podge of cuts going into ground beef, and avoiding it, is a matter of taste and, remotely, control of fat content, although that is roughly measured and adjusted after each grind batch (Im not sure if that is a legal labeling thing by now).
As for safety it makes no never mind.
In Italian that would be al sangue or “bloody”. A writer once wrote “If you go to a restaurant in London, please don’t ask for a bloody steak” :smack:
It isn’t that risky to eat. You’re probably more likely to get generic food poisoning at any random restaurant, or be injured in a car crash getting there.
There are some that do that, or at least grind their own beef from whole cuts sourced from known providers. Those places will typically sell you a less than well-done burger without comment.
But the vast majority of burger places use one of two more common options- either pre-ground fresh beef (of varying levels of quality), or frozen burger patties that they cook. Either of those options presents food safety issues, since you have multiple animals coming together in one batch, and because one dodgy piece of meat can contaminate the entire batch.
So the USDA guidelines are to cook it well done to eliminate any bacteria that might be present. Many restaurants will ask you how you want your burger, but in my experience, you end up with medium-well to well, regardless of what you specify. Part of it is due to the places having relatively thin patties which are hard to actually get a good sear on and yet not overcook the burger, and part is because I think they deliberately cook to at least medium-well regardless.
The word is sanglant = bloody.
I’m a medium-rare fellow myself on burgers and steaks, though I do love a good steak tartare. My in-laws like to order what they call “charred rare”–rare but with a good hard sear, which I would guess corresponds to bleu. Can’t remember if they do this at every steakhouse or just at Morton’s, where they like to go for special occasions.
This Cowboy version is similar to the Clint Eastwood Quote I remember,
Years ago I learned that at 95% of coffee shops and diners, if I want a hamburger not cooked to death I always order “rare,” and hope for the best. Only once I think has it ever come back rare, which was OK, I guess, but with shitty coffee-shop hamburger meat is not so nice.
ETA: And I love steak tartar in the classic Western style and the Korean thingie with garlic, sesame oil, and (Korean) pear…
I’m glad I didn’t run out and order “Un ‘bloody’, saignant s’il vous plaît” 