Big fan of Max Keiser too ever since I discovered Russia Today.
I'm also a big fan of Have I got News for You. Didn't realise he'd been on, will have to catch that episode.
Been to a few filming of HIGNFY and yes they film a lot, and keep what they best judge to be funny and is required for continuity. They have a team watching for the final edit and sometimes re-shoot a few bits at the end (normal the guest hosts bits) too to improve on the original takes and improve continuity.
Who says the camera never lies.