Yes, Ts can ethically have those kinds of feelings for their clients, and many do. The ethical grey area is in what they do with those feelings and how/whether they express them to their clients. I don't think your T did anything unethical, anyway. Having said that, it's clearly stirred up some strong feelings and confused thoughts for you so in that sense perhaps it's something she shouldn't have expressed so seemingly thoughtlessly.

The only way of knowing exactly what she meant is to ask her...