I'm not challenging your site at all, Sir GH, so please don't take it that way. I haven't heard the Richfield show, so I can't comment there, but I do know that on the ANATO tour boots, it's very easy to tell that Freddie is actually singing the line offstage.
Your theory regarding Freddie overdubbing the line in Earl's Court makes sense, especially if it was an official release candidate (and, God willing, will be again). There's one question I'd need answered there before I could definitely chalk that up to a studio overdub, though, and I'll pose it here:
Assume Queen were cleaning up Earl's Court for an official release, but the project fell through. What bothers me about the after-the-fact recording of the line is why the band would choose something as simple as overdubbing a line in Bo Rhap to fix before they tried to overdub the microphone dropouts in TYMD?
Another reason I'd be more inclined to believe that Freddie actually did sing the line live: it was a special show in their hometown, right at the end of a tour. Queen has been known to pull out the stops for tour-ending shows, especially in locations as special to them as London and Japan (example: My Fairy King and MOTBQ being played as part of a piano medley in Osaka '85). They certainly pulled out lots of stops for Earl's Court, debuting the crown rig, reviving Procession, and covering Saturday Night's Alright for Fighting. Maybe having Freddie sing that line live was just another nod to the fans?
There's one aspect of that argument I can't rectify either, but I'll leave it to more experienced ears (such as yours, Sir GH) to make that distinction. Freddie's voice is much, much clearer during that line than at any other point in the song. Whether that can be attributed to singing over a backing tape as opposed to over four instruments competing for decibels, I don't know, but it is worth mentioning as a possible studio overdub hint.
Enough about Earl's Court. Back to Houston. I'm feeling rather stupid admitting this, but I can't find my FLAC of the Chicago '77 show. Seeing as how it happened less than a week before Houston, I think that would be our best bet as to determining just what happened at Houston. No one argument makes perfect sense. Because Freddie wasn't typically singing the line during that tour, one good guess is that someone picked up the wrong backing tape that night.
The obvious flaw in that logic? What the heck was the ANATO tour's backing tape doing in Houston? If they had accidentally brought it along instead of one with the line in there, wouldn't they have noticed before they got a month into their world tour and made a call back home to have the correct one sent over?
You could also argue fairly convincingly that they brought multiple backing tapes for Bo Rhap. Tapes wear out, and playing the same 60 seconds of it every night--not to mention rehearsals--would be a good way to kill it. Again, the question of why the heck the ANATO tape was brought along (and how no one noticed during rehearsals) is raised.
My best guess? Here goes:
There were 26 NOTW shows in the United States. Of those, we have five concerts preserved either in full or in part. It's entirely possible that the band brought that tape along, and Freddie would decide the day of--hell, maybe even during Brian's guitar solo--if the audience had been energetic enough to earn a special treat here and there. It wasn't unheard of for Freddie to do such things.
There's another unusual aspect to that operatic section, and that's Freddie's entrance at the end. Granted, our video record of that era is small, and the band wasn't doing the lightshow yet, but Freddie's entrance through the smoke as the operatic section was still rolling was unlike any other one I've seen him do.
My "official" theory then, which will no doubt be torn apart and debunked by those more qualified to make such assumptions, is as follows:
Sometime on that tour, Freddie d
"Do you think I should keep this mustache? Did you say no? F--- off."