Well, he's been called to Nadler's judiciary committee under the auspices of congressional oversight inquiries on the Mueller report. Nadler just changed the rules of the game after the cards were dealt by wanting the democRAT members' staffs to question him, instead of the congressmen themselves. That's why Barr balked.
Call it what you want. Congress still has the authority to question him under the proper circumstances.
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.