Any sworn testimony given to either branch of Congress is subject to penalty of law, including perjury, and the whole gamut.
And when it gets into classified info in closed sesion, I imagine the penalties only get worse.
Why were Senators making a big deal out of putting Alberto Gonzalez under oath? That wasn't a court of law either. As I recall, DICK Durbin was the one wanting him under oath.
After what's already happened to Lt. Col Shaeffer, he'd be a fool not to have counsel. If you've watched many hearings, everyone who goes before congressional hearings to testify always has counsel.
My guess is they aren't allowing him to have counsel in the closed hearings because of classified issues, but that's just a guess.