Unfortunately the world is filled with exceptionally skilled con artists, abusers, criminals etc.
It is so easy now to give yourself a clean slate.
I have kids and I know two of them are not the best when it comes to judging people.
If I could protect them by getting a prospective partner checked out. Your damn right I would do it.
And I wouldn't feel guilty about it either.
Having said that I wouldn't make secret of it. I would let them know up front. Give them a chance to come clean if necessary.

Her family are obviously very concerned for her welfare and I would be more concerned about the fact Tey feel she has such a massive flaw in her ability to judge people than I would be afronted by their checking me out.
This is a family that is likely to feature very heavily in her life. And that she is likely to complain every upset too.
This can make for some exceptionally uncomfortable dynamics.

Can I ask is she independently wealthy or in anyway tied to her family financially. ?