Well, based on the Nixon precedent, the answer is Yes. Where there is communication that relates to a possible criminal matter, or misdoings, then all communication is fair game. As well Congress subpoened Bush's records investigating "torture."One basic question is, How can Obama both invoke Executive Privelege to cover communications AND claim there were no communications? Either there were communications on the matter or there weren't.
The second question is why libs deflect to: Republicans lie more. Boosh! Cheney! And other red herrings. We aren't discussing those things. We are discussing the actions of this president. There doesn't need to be "proof" here. There needs to be reasonable inference. The reasonable inference of a claim of EP is that there is communication to be covered. The reasonable inference of the WH saying there was no communication is that there is no need for EP. The reasonable inference of the WH claiming both things simulataneously is that someone is lying about one of those things.
The question is, do the president's enemies get to sort through all his communications in the Oval Office?
Doesn't matter if they are sorting through everything because he says there was "no" communication or some communication. The issue is, do the president's enemies get to go through all his communications on whatever ground they can think up next?
Executive Privilege says, no, they don't. That's private. I agree.
Again, all of that is irrelevant to the question here: Either there is communication or there isn't. But the WH cannot claim both simulataneously.