Out of curiosity, do live concerts that are broadcast in HDTV typically make separate 5.1 channel and 2.0 channel mixes, with separate recording engineers in charge of each? Or do they make a 5.1 channel mix that is automatically downmixed to 2.0? Or a 2.0 mix that is processed in some way to create 5.1?

The reason I ask is I have watched many live (or live to tape) musical performance broadcasts. eg. American Idol, random stuff on Paladia. Sometimes, the 5.1 mix sounds great and the 2.0 mix sounds terrible or vice-versa (I can change which audio program I listen on my AVR). Sometimes they both sound good and sometime they both sound bad.