It sounds like your T didn't say hi because you didn't notice her and maybe she thought you did, but you were deliberately ignoring her. She's right. It WOULD be a boundary violation to approach you unbidden. However, I think the fact that she said something is a little bit of a boundary violation too although with your best care at heart. I don't think she's checking your boundaries but maybe she is worried about you.

Are you worried about her seeing you? Would you want her to approach you? If so, then go ahead and tell her. I think the only way through is an open and honest approach.