The danger with stating this in terms of absolutes like:

> no support group from a big company is going to call you. Ever.

Is, eventually, you probably will get a call from a support group at a big company, as many have noted in response, and then all of the other absolutes in the list also become "well, people say never, but I think this is one of those exceptions" instead of "it's never worth taking the risk of assuming it's the company who really called you".

A company, even big one people joke about having a complete lack of actual human support agents, may really call you one day. The other 364 days of the year it's probably a scam. The safe bet is to take the issue they called about and contact the official support channel yourself (being careful to get a real one and not an ad/fake site if you need to Google it). It may not always seem the most convenient, but it only takes one mistake to end up in a much more inconvenient place one day.