You still didn't answer the question. How old is she and how old are you?
Dont think the parents sound overprotective at all. They sound legitimately concerned as would I.
Honestly, this is creeping me out a bit.... If you were 20 and she was 17, I'd still be hesitant.
Their brain isn't fully developed at this point still. There's a reason why under 18 is jail bate.