Good work. On your transcription: it's "Verify gate A57", not "Verify you're a 767".
And both ways of issuing landing clearances in visual conditions have their advantages and drawbacks. At moments of peak traffic, expect clearance on short final means that the a lot has to go right in a very short period: the previous aircraft needs to vacate/get airborne, and the controller has a very short window to get the "cleared to land" call out. The lack of that call in some cases will be the sole cause of a go-around, and that go-around will occur precisely at the moment of peak load on the controllers.
In any case, in this event, it's entirely irrelevant. 28L and 28R are very close together, and the angle from tower is insufficient to distinguish between what runway they're going to land at until they're very close in; sidestepping happens "all the time" at SFO, but only under conditions where the safety can be insured. The United crew saw what was happening, queried tower ("Is that airplane going to land 28R?"), then challenged ("Are you sure?"), then took action; the AAL crew at the same time had several visual and radio cues to go around (The Line Up and Wait might have sounded routine, but United's query most certainly got the attention of everyone on frequency), and they probably were already on their way when tower made the call. In this case, a short final "Cleared to land" call would have only emphasized what was obvious.
Either set of rules, the folks at the pointy end have the authority to keep things safe. ATC can only help. Everyone did their job.