From my now much former radio and television days, I know from real life experience that shit does happen on live shows that usually somebody in the viewing/listening audience catches and justifiably criticizes. Sometimes even in the movies that undergo dozens if not hundreds of viewing, editing, tweaking, etc. before they are released to the public can have glitches the editors miss, most especially when scenes are reshot and then segments are spliced together. Even on the newspaper, we were sometimes chagrined to see the wrong photo used for a story or the wrong caption applied and the proof readers missed it before it went to press.
I am pretty confident that was the case with these obviously mis identified videos--probably some rookie stage assistant inadvertently mixed the clips. But Stewart certainly was not out of line capitalizing on the error and Sean did as classy an apology/correction as possible without insulting Stewart in the process.
I've never seen anything comparable to that on MSNBC, however, when their misrepresentation of the facts have been noted and pointed out.