It seems to me that there is really no perfect solution in this matter. It is not really the openness of the commission that discourages conspiracy theories - the commissioners could talk all day long and people could say they were suppressing other information that they did not talk about. In reality, it is the very politicization and partisanship that discourages conspiracy theories. To the extent that it becomes apparent that the primary motivation of the members of the commission is to do all they can to support their political allies and hurt their opponents, it becomes less likely that they are suppressing evidence that would aid these endeavors.
My feeling is that the openness is merely revealing partisanship that would have existed in any event, which is a good thing. Most people who have any opinions at all about politics are going to be biased in this manner, and there’s no sense of quieting them down so as to allow them to pretend otherwise. The only way to really remove partisanship from such commissions would be to find commissioners who were truly apolitical, but such people will be inevitably be extremely rare.
The only real downside to all this openness is in that it provides a temptation for grandstanding by the commissioners. Even for politicians, the ultimate loyalty is not to party or ideology - it is to themselves, and to the extent that you give people an opportunity to make themselves seems more important by all sorts of posturing they will take it.
But the bottom line is that people are people, even if they happen to be appointed to commissions. The value of a commission is more in the information that it can elicit rather than in the conclusions that it draws. So whatever the commissioners do to their credibility is of relatively little consequence - others can make their own decisions.
Unless genuine state secrets are involved (such as the identity of undercover CIA agents – CoughAhemValeriePlume*Cough), I can’t imagine a situation where there would be too much openness in the workings of a democratic government.
Put it all out, warts and all, and let the electorate decide.
On a day-to-day basis the partisanship can be pretty disgusting, and it makes for great, sensationalistic headlines. But people have short memories about this sort of thing and the negative aspects of the open hearings fade pretty quickly. Seems like a small price to pay for public hearings give the alternatives.