First, who the hell was that who swore Biden in? She wasn't even a member of SCOTUS, much less the Chief Justice. Does the Chief Justice usually do it just because of precedent or is there something somewhere that says he or another member of SCOTUS has to do it?
Second, regarding the rumors that the broadcast was shown a full 8 hours early in Spain (multiple reports of that so far it seems), I will say this: I was stunned when I turned on my feed to it and it wasn't yet noon and Biden was already delivering his speech post swearing in. I remember thinking at the time how odd that was that they had done it early, even if it was just by a few minutes.
Thoughts on those?
There is a fair amount of evidence that it was all done a day earlier, and required the editing of many "takes" to get a coherent oath of office out of Bi Den. This explains the magic disappearing teleprompters, podium and people during the "live" broadcast. That also explains how Spain could get a copy 10 hours before it was supposed to be held the next day.