I agree the House has that authority. I believe the house will say...okay...we want you and the Congress folks will question you.
Of course, the staff (which are all attorneys) will furnish the questions. The House has to save face on this one.
I read somewhere that Nadler said he would make Barr another offer to testify or he would issue a subpoena. So I'm sure the deal was without any staff questions. Otherwise, Barr would pass again.
Barr's the one with the upper hand here, not Nadler. Nadler is just an inept tool of the democRATS. Barr is knows how to handle himself.