I have mixed opinions on what he's saying. I think a lot of it depends on what kind of nuclear technology was used. A lot of people think of all nukes being like the ones we tested publically, or dropped on Japan. The thing is that nuclear technology has not remained static after that point. People tend to forget how many nuclear tests are done underground and in isolated locations by various nations, both secretly and outed.
The truth is that today's nukes can acheive a variety of effects. What's more in a truel "World War III" scenario, nukes are not the only weapons that are going to be brought into play, rather they are going to be used alongside chemical and biological weapons, as well as things like the infamous Neutron Bomb.
A lot of it also depends on interception technology which people tend to forget about. ICBMs are on the verge of becoming obselete. The US has freaked out Russia by demonstratng some of it's tech which violates treaties with the USSR, and China has been using ground based lasers to blind satellites which means that they could use it to stop (or seriously hamper) ICBM strikes which require targeting with satellites and computers, sure there are other ways to target but none that are "automated" in the World War III sense. (and if you don't believe me on the china thing, do a search for the key words China, Satellite, and Lasers).
The scenario in Fallout becomes a bit more plausible when you consider that our technology is a bit more advanced than the Romans, especially our record keeping. We aren't going to have a lot of barbarians running around burning books 15 seconds after the war, and people aren't going to degenerate that quickly. What's more the Fallout games take place in the US where for the moment we have a technological edge, and are liable to fare the best out of anyone in the world, barring some kind of "survival by omission" like what happemed with Africa in Heinlan's "Farnham's Freehold". Indeed by some estimates if the US lost all allies and engaged in an all out war we'd have between a 20-40% chance of surviving relatively intact (though with a lot of damage), on the other hand the rest of the world would have a 0% chance of survival because we have enough firepower to kill everyone on earth with WMD 10x over. In a real scenario however the US would have allies, and a lot of allied nations who weren't stupid would have defensive bases like the one Russia threatned to nuke Poland over which would give them abit more coverage.
The point being that the "OMG, nukes hit the ground and kick radiactive dirt into the air killing everyone!" scenario of past decades isn't quite accurate any more. The nuclear nations with weapons that crude are also among the least likely to ever be able to successfully hit anything either due to lack of delivery systems, or simple interception. A nation with a half a dozen nuclear warheads or whatever isn't exactly going to saturate a defense grid.
In short he'd need to provide more information IMO, I confess to not being an expert, but this seems a lot like he's using the same assumption as movies like "Wargames" without taking progress into account. Indeed one of the big fears for a lot of people today is that nuclear weapons are going to become entirely obselete due to defensive systems making delivery almost impossible. That would end the nuclear umbrella ensuring world peace (no more MAD) and bring us back to an age of conventional warfare... and when you look at the amount of conventional forces nations like Russia have stockpiled, and China is building up (complete with boats to deliver them) while nations like the US are downsizing and increasingly putting their faith in technologies that might be going in the wrong direction... well things could be getting interesting.
In the case of Fallout, this is also a world where there was an alternate history. We have powered armor, personal energy weapons, giant robots, and cars that were apparently running on nuclear generators by the lore. Who knows what kind of defensive systems were in place, or what kind of payload those nukes were actually carrying, or even what the intent of the people firing the nukes was. Did they hit the ground to try and stir up a lot of radioactive fallout (like the name of the game), or did they mostly airburst?
Given that the two superpowers were the US and China, it's not surprising that areas like DC would have survived, because they would probably have had some of the highest concentrations of defense since this war was a "slow burn" one instead of one that went nuclear immediatly. It started with conventional warfare, and got worse.
Just a lot of rambling thoughts, the bottom line is that I think Fallout is a bit more plausible than he gives it credit for, especially seeing as we're dealing with a science fiction universe where while a lot of things are "retro" they also have technology that is far more advanced than anyting we have in reality.