I think you're raising a false dichotomy to assert that the situation is either a Constitutional issue or a case of corrupt Congressmen trying to cover their butts, but not both. It is both. It's hardly the first time that respect for the Constitution has placed us into the difficult position of having to choose which of two principles to defend. My view is that the Constitution represents a higher value to be defended, even if, in the end, we have to let a crooked Congressman escape justice. Rationalizing away the Constitution a little bit at a time in the name of expediency is the road to ruin.

Congress and the Executive branch don't have symmetrical police powers--the Capitol police have a narrowly-circumscribed jurisdiction, the Capitol grounds, and can't go raid the White House and confiscate documents. The FBI, of course, has national reach and jurisdiction. Congress is definitely in the inferior position when it comes to the use of force, and I can't imagine that the Founders intended one branch to be vulnerable to the use of force by another.

Just as there are competing values to weigh, there are competing evils to judge. That there's a culture of corruption among Republican politicians doesn't justify discarding the Constitution (see first paragraph). There's also the corruption of the Executive branch to consider, including its impermissable assertions of power. We can't argue this in a vacuum, we have to discuss it within the broader context of the illegal NSA wiretap and surveillance programs, the signing orders, refusal to cooperate with Congressional investigations, and on and on and on. Add them all up, and if it hadn't been this particular issue, another one would have come along soon enough which finally forces even Congressional Republicans to say "enough!".

We can't fix everything simultaneously, so we have to make value judgments to set priorities. First we rein in the Executive Branch, then we rein in the Legislative. One step at a time.