[Bruce Campbells Chin]

The internal rules to which you refer are not mandated by the Constitution -- the Constitution says they literally are whatever those houses say they are. That means they can be changed at any time by the majority, which is what happened here.

Slimy, but perfectly legal.

[livius]

The House changed the rules for their hearing specifically to prevent the GOP from calling or interrogating witnesses, and also instituted the secret proceedings, something never done before and something that would be blatantly unconstitutional in a real legal proceeding.

So yes, both Houses can make their own rules, and the GOP could theoretically do the same in the Senate. But they won’t, so we shall see.