"Both browsers make it fairly clear to anyone who bothers reading the error message that the site is "obviously not a fake".
A fair point, if you are prepared to equate reading with understanding. There are just three problems.
Firstly, "security certificate", "trusted certifying authority" and "name" are jargon terms. Replace them with pitchfork, gardener and carrot. Now re-read the error messages and I think you'll find that it is no longer obvious that the expiry failure is less serious than the other two.
Secondly, whilst I have accepted certificates under these circumstances, my "advice to grandma" would always be "If there's a problem, don't accept it.". I *hope* that the vast majority of web users default to mis-trusting institutions who can't keep their paperwork in order. (I doubt it, but it is something to wish for.)
Thirdly, *I* wouldn't accept this certificate for online banking. If they can't even get this right, what else is wrong? This is my money we're talking about. I'll wait a couple of days. If they fix it, that's fine. If it is still broken several days later, I'm going to start looking for a new bank.