That's way harder than just asking someone to do the exact thing that they've already done over and over on your legit site. Sure, some will still fall for it, but the bite rate will go way down.
Phishing attempts by definition create artificially urgent abnormal situations whose job it is to convince the intended victim that they're legitimate. A difference in degrees like this strikes me as not really something to haggle about. Users who fell prey to the attack aren't going to be reassured on hearing how much more unlikely it was.
