I wasn't clear enough, and we don't really disagree. The cross purposes, is about the "can't" people, saying, you can't say it in one given situation (which situation is in their head, and they're right about that one), where the "can" people are saying you can use it (in another situation) so they're both right, but they're not always communicating what situation they have in mind. Still not sure that's any clearer, but it's my best shot, this late at night.
Those that say "can't" are correct, in my variety of AE, if they are referring to their neighbor at the picnic table holding a pitcher of beer in one hand, and a pot of tea in the other, and offering them a drink. "I'd like a tea" is not possible in this context, you must say, "I'd like some tea" (ditto some beer).
If instead of bulk containers, their neighbor reaches down next to the picnic table into a large cooler full of bottles of cold beer and iced tea, then "I'll have a beer" is fine, "I'll have a tea" is fine, too.
So when you (or anyone) says "'you can' and people do!!" my point was, "Yes, sure, but it is context-dependent, and both are right under some circumstances, and it is equally true that both are wrong under other circumstances.
I was trying to point out that it's not as simple as "you can" / "you can't".