I don't think that it is that strong a claim at all, not all vehicles are used to the same degree by their owners, every second hand car website can tell you that.
Cars that are 5 years old can have anywhere from 20K to 300K km on them. It all depends on the usage.
Lots of good data here:
http://www.solarjourneyusa.com/EVdistanceAnalysis7.php
People using their cars for 50K to 70K km per year are not exceptional (professional use), private individuals using their cars for < 5K km per year are not exceptional either.
You didn't claim 'not all vehicles are used to the same degree by their owners'. You claimed that if a report says 77+% of cars could be electric using the current grid, it probably means the least-used 77%. That's the strong claim.
It's the claim that makes most sense. You'd take the least used vehicles because their usage patterns will match current production EV sweet spots best (always assuming we are talking 100% electric and not hybrids).
I won't use the word 'extraordinary', but that's at least a strong claim, so needs strong evidence to back it. Why wouldn't 77% of vehicles mean 77% of the load?