Yeah, they vary a lot. Yet they don't vary 300 points a day unless you have just started to play here. Once you played a lot of games here, your rating varies only a little, maybe by 8-10 points per game. The same story is with OTB ratings (Actually, you won't be rated until you played a certain number of games in OTB tournaments)
Yes, your rating can be deflated and inflated by around 200 points. However, it's more typical for amateurs. People with an ELO of 2500+ don't experience such huge jumps even in bullet games. So, 2500 GMs don't reach 2793, not by a long shot.
This is a funny post. I think going from 2500 to 2793 is more difficult than earning a billion dollars unless you are a very young 2500 player. Going from 782 to 1075 should be done in a matter of one month or perhaps a few months provided that serious long games are played.
If someone dabbles mostly in bullet and blitz games, then going from 782 to 1075 is very impressive. In other words people who play very fast controls should not go up. Well, maybe they should go up a little bit, but not much.
If you've gone up only on bullets and blitzes, it is indeed very impressive!