I'd tend to agree with your interpretation. Trump was asked "are you willing tonight to condemn white supremacist and militia groups and to say that they need to stand down" and he immediately said "sure I'm willing to do that". Biden supplied the name Proud Boys and Trump replied "Proud boys, stand back and stand by". It's Trump's usual awkward way of expressing himself. The phase "stand down" was said earlier so to his mind, he thinks he's agreeing, because he's just said he's willing to condemn these groups a moment before.I thought by “stand back and stand by”, he meant, don’t get involved, just watch.
Did Wallace put the current violence and ANTIFA to Biden? What was his response? It’s known the Kamala Harris backs it, but how about Biden?
However, I think if he'd said "stand down" the press would still all be over him as it'd be spun as an admission that he calls the shots with these groups: "Trump orders white supremacists to stand down!" Like I said, he was on a hiding to nothing.
This reminded me of the time it was reported that he was suggesting you injected yourself with bleach to ward off Covid-19. I thought that sounds insane, and checked out the clip - and of course, he wasn't saying that, but it could be spun that way, so it was.
Re Biden condemning Antifa, he came out at the start of September saying he condemns violence across the board but never mentioned either Antifa or BLM by name, so it was a bit rich him insisting Trump specifically condemn named groups when he's never done it himself.