if this decision had gone the other way - it would have been. it would be the only branch to have a constitutional protection against oversight from the other branches. and not for legitimate actions mind you, I agree that is in the constitution - but for EVERY KIND OF CRIME. the executive and judicial bracnhes have impeachment and removal, so who oversees congress if the law were to be as you suggest?
and don't answer with - "the voters", or "they investigate themselves".
Still, notice that the Constitution provides that the House and Senate are judge of their own members.
In questions like this the Founders fell back on the elected body closest to the people to decide how to proceed in the case of a crime involving their members.
You might well read the Constitution someday to check all of that out.