Come on, she wouldn't even look at Ilya at school and wouldn't deign to participate in the same picture story (or whatever) project. She might be socially awkward, but this episode surely gave the impression she's totally looking down on Ilya. She envies Ilya's power but hates her uncontrolled personality that occasionally make the high power a liability (in Miyu's opinion, that is), not an advantage. So, in short, she thinks Ilya has no business collecting the cards and thus is not worthy of being a friend outside of the business either.