Thanks for the reply.

I thought there'd be rules, but it seems the Alitalia rep isn't aware of them. She as very certain that it only depended upon:

(a) The plane is not full and has open seats (of course) [Not checking bags and being present at the airport/departure gate are also basic requirements]
(b) The agent deciding to allow you on the earlier flight

Without (a), then (b) is irrelevant. But even with (a) she said there is no guarantee that the gate agent would put you on the flight [unless you pay a change fee and difference in fare].

If fare class matters, then I'll have to call back and find a rep that evidently knows that rule.