"Seeing as how she wasn't onstage at the Broadway Theatre, wasn't in costume and wasn't supposed to be in character (as was argued over in recent weeks- this was about celebrating the Atlanta Alliance theatre, not about promoting The Color Purple), you can't claim her crying had anything whatsoever to do with her acting."
That's what makes her so unique, it's what makes her a slam dunk success on Broadway in both acting and singing. She knows her reviews have been spectacular raves, she knows that people wanted to see what the raves were about, so, even not in "character" she still gave the people a small piece of what they might experience on the broadway stage. The tony stage is way more fitting for that then an Idol stage. The only way your argument would hold water about her not being in "character" would have been if she sang a song that wasn't a number that she does every night in TCP. She might not have been in costume but she was still in character during a portion of that performance. It's probably out of habit by now though, after 73 performances it is kind of hard not slip into character doing that number.
Here high level performance skills are why we are able to get shots like the one below. Now I can tell you, this isn't something she normally does when she performs. When she usually performs as herself, she's usually bend over or dancing and walking all around the stage and she rarely ever cry's when singing and her standing in on spot almost never happens. I've only seen her cry when she sang "I believe" and "I'm Here".