I did not see the video stream myself, and have no inside knowledge on this at all, so this is just my opinion but;
Nobody releases a live album that hasn't been touched up in some way. If they do, they call it "an official bootleg".
DT has the benefit of having recorded every show they've done for decades now. For the past ten years or so, it's multitrack protools sessions... Which means, if they need to fix a flub when they compile a live release, they can actually just go down in the archive and fetch a track from a show where it sounded good. This is why they recorded two shows for the Distant Memories tour, so what you hear is actually a compilation of the two nights, although most of it is the night that is most filmed. That also allowed them to get a multitude of alternate camera angles with a smaller camera crew...
Budokan was never even supposed to be a dvd/live release, it was meant for TV only. So the attention to detail wasn't AS HIGH as it would be on recording a show for a full on physical release like Distant Memories. The TV version had a very noticeable effect layer on James voice, and I would assume they wanted to fix that for the stream. How they did, dunno. But yeah, there's all the common tools everyone uses - alternate takes, overdubs, pitch correction. Let's not pretend that's not industry standard at this point...