Wait, where did you get this? She obviously doesn't care about friendship. She just stated that she didn't care who gets the solo, despite her friend being part of the selection. If she loved music, she would answer that the better one should get it. But she said she doesn't care at all.
Remember her blank eyes when Sapphire was talking about friendship (it was about friendship, not romance, because she felt guilty for pushing her friend)? Yeah, Asuka is not caring. But she goes and speaks with Kaori to make her feel better. Two-faced.
@Ryll - I'm actually not sure. I'll hold off til we see next episode to see if your interpretation is correct.