In Battle of Gods, Beerus states that he had to use 70% of his power to fight Goku at the peak of the fight.
I'm guessing that's just anime filler, because it's contradicted by virtually everything you learn during the ToP.
Nope, that line was also in the movies and Toei simply incorporated it into the series.
The problem here is that between the movies and the serialization of Super's manga Toriyama decided to retcon a few things from the movies. That's what has been retconned in the manga from the very beginning:
1. Bills being that close to SSJGod Goku.
2. SSJGod powers being incorporated into Goku's base state completely (the base state gets stronger but still below any SSJ form, and the SSJGod transformation becomes available to Goku instead).
The problem with the anime is that it began following the logic of the movies and in the end it had to end following the "logic" of the manga (well, trying to do so at least, because Toei's writters are awful) so the first sagas contradict a lot the last ones.
Regards!