There is a lot of concern these days about teacher/student relationships outside of normal school activities, with some justification. There are indeed predators out there, both among the teachers and the students.
That said, there have been a great many teacher/student interrelations outside of school that have done no harm, or actually were beneficial.
She's an odd case. I don't think she has it in her to be a predator of that kind; she's not in-person aggressive that way.. But she is correct in thinking that there are those who would disapprove of such contact as they are discussing. Setting up an alt account just for such contact would actually be worse if found out than doing it with her main account.
I do hope things work out for them in the end, however the relationship develops.