I'm exactly like you... I have told friends in the past that I tell DH everything (meaning I don't keep secrets from him), so anything they tell me has that caveat.
My close friends know this and one even said to me once, 'I know you'll tell DH, but just make sure he doesn't say anything to anyone else' - when it was about her DP who shares lots of mutu friends with my DH.

This may not be what everyone is like, and that's ok by me, but it's how I choose to be in my relationship and so if someone doesn't want my DH to know something, they shouldn't tell me.

My MIL even once tried to tell me something and said 'but don't tell DH'... I stopped her right there and said I can't do that.

I think the potential for her DH to ask you questions throws a spanner in the works though. She's put you in a very difficult position. But why would he come out and ask that? Is he suspicious or is she just super paranoid?