The second argument in the original article explains that rats have been observed rescuing their young from similar wildfires in the past, which suggests rabbits might do the same during similar situations. Making such an implication using two very different species based on what is essentially anecdotal evidence, however, is a tough sell – particularly as rabbits haven’t been observed doing this on any occasion.
As aforementioned, burrowing rabbits have high survival rates. If the rabbit did have a litter, then as long as the man released the rabbit nearby in a place of safety, it's likely that it returned to the populated burrow when it could, and all would be well.
Incidentally, it cannot be confirmed at present that this was actually a rabbit; it could have been a hare. Unlike rabbits, hares don’t have burrows, and studies have shown that wildfires do kill them. If the animal in the video was a hare, then perhaps he did save its life.
In any case, experts suggest that, in general, when it comes to most wild animals, they should be left alone regardless.
“Fire is something animals have to deal with constantly,” California Fish and Wildlife spokesperson Peter Tira tells SFGate. “Fire or no fire, just let the animals be.”
An article on Slate opines that saving the life of one wild rabbit wasn’t worth it because it put the man’s own life in danger. The rescuer may or may not have done a good deed, but perhaps it’s irresponsible to encourage others to endanger themselves in the same way.
At the very least, though, it is harsh to lambast a solitary individual who put an animal's welfare above his own.