Not at all, it's her responsibility to know when to stop. Yes the bar should also step in and stop her if they deem it necessary, but first and foremost it is always the responsibility of the person to make sure they're not doing something stupid. Or at least if they do, that they won't whine if they get themselves in trouble through it.
Since when did the idea of personal responsibility disappear? Do you really want every single move we make to have to be approved and checked before it's done? Let people make their own choices, but if they do something stupid then the blame is on them.
The facts are that her drinking enough liquid nitrogen to do her serious harm happened on a licensed premises with precisely that responsibility.
One of the main reasons premises are licensed, is so that consumers can be confident they're not being served poisonous drinks, everything on sale is traceable, quantifiable and served in specific measures.
It is not her responsibility to check if the ingredients of a drink, served in a bar are an immediate health risk. That is entirely down to the licencee to ensure, otherwise they'd be in contravention of their licence and normally, it's safe to assume, licensees don't serve drinks which are in contravention of their licence.
I know a pub where someone drank nearly a pint of line cleaner and ended up in hospital. Now the person who drank that ordered a pint of beer. A pint of cask beer. They got a pint of clear liquid that looks, smells, and tastes like line cleaner. Which they drank.
Now I'm going to say that if I did that, I'd think myself very stupid. Drinking a pint of line cleaner is a very stupid thing to do. But this person did, and quite rightly got a large pay-off for being made very ill. Why? Because the pub shouldn't be serving people line cleaner. It's overwhelmingly the pubs responsibility to not serve people line cleaner rather than the customers to say "hey, hang on, this beer tastes funny".