As already mentioned, an induction at 10 days overdue is very normal. So that isn't very surprising.

I think the strange thing is that the OB is talking about a date already! It may be standard that he induces at 10 days and it kind of goes without saying that any OB is going to want to induce if you go very long past your due date. It just seems to be a lot of extra stress to put on your SS to be given an induction date before she is even due.

I think the problem here is an OB that isn't particularly sensitive with what he is saying. I would encourage your SS to do all the things that are supposed to bring on labour and then inform herself about inductions if she does end up going over her due date.

No point stressing too much now.