AT&T is not buying Yahoo and Yahoo is in the midst of shutting down all of their POP 3 accounts and shifting them to IMAP. The other situation the tech was referring to, and many people have been facing, is problems with Yahoo's authentication servers. This problem has been going on longer, back to about 2004. Or longer. I experienced it in Entourage on a Mac and in Mail.
What Thunderbird is doing is "bumping" Yahoo's authentication server and then the Mail client works for awhile. You can probably do the same thing in reverse order, start Mail first then use the Thunderbird client.
My resolution to this in 2005 was to permanently forward my Yahoo mail to my .Mac account. Never have had problems since then and don't have to listen to Yahoo support tell me they don't support Macs (or iDevices now). Other people I have spoken with say the easiest route is to use the Yahoo mail app but even then their mail will sometimes just stop for awhile then restart.