I'm sure that the energy providers can pull a list of affected streets and areas etc but all you can really confirm would be the property owners who have their name on title or tenants under a lease agreement. Since the claimants don't need to be registered for Government assistance surely just about anyone can come up and say "yeah, I live in [name of no power] street".
I'd imagine you would have to produce utilities bills, mobile phone bill etc to substantiate residence and if you can't produce something like that, too bad! Really though, that just takes us back to exactly what you mentioned in the last post.
It couldn't be good PR for a Government agency to pull people across the coals to prove they have been disadvantaged by a natural disaster and just as bad to prosecute people for suspicious claims, even if it is years later.
Either way though, its an expansionary fiscal mechanism. People will spent that money just as quickly as they get it. Most will spend on repairs and cost of living and some will squander it - regardless, they'll shove it back into the economy and not save it - it helps put a floor on any possible downward pressure on GDP.
Anyway, just out of (morbid) curiosity - how much do you get for loss of a loved one? Imagine being the government employee that had to put a dollar figure on that one!