To be totally honest with you, the dealer is full of it. I say that all it takes is a very small amount of air in the system and the engine WILL NOT RUN. I've ran into this issue numerous times over the years.
In fact we're right in the middle of a power outage, and I just got done chasing an air leak on my diesel generator. I found a couple of possible leaks, but nothing that I could really say was the biggest problem. So I just redid everything that looked suspect, and made sure I took care of whatever was wrong.
Before the engine wouldn't smooth out, but rather would set there and hunt/surge slightly. It was just enough to screw up the voltage it was producing by a little but, but any is too much. Now it's running smooth as butter again.
Again I've run into the problem many, many times, and air in the system is not your problem, as air will cause you to not be able to run the engine at all, for it to hunt at all speeds, for it not to be able to handle a load. I've seen every one of those happen art one time or another.
Now what may be happening is the internal supply pump got worn or, if it has an external supply pump, it's not putting out. The injection pumps needs a constant supply of fuel to build pressure inside the pump housing. If the supply is too low 'vapor' will be created. It's not really air, per se, but that may be what the dealer is talking about. If that happens past a certain degree the pump would still should not work properly, and the engine would not run properly either.
In any case check out the link to read any and everything you might want to know about a VE pump
Personally I believe the biggest problem is the simple fact the diesel fuel now is pure crap. The 'industry' can say all they want about it being as good as it ever was, but when your out in the field seeing the problem across equipment lines and brands, and hearing about the problems from multiple sources (including the fuel shops that love it, as they profit from it)it becomes clear in short order. The only thing I know to tell you to do is if your not running any kind of additive, is to start. I know customers and other folks that run additive religiously, and others that you can't convince to do it regardless of what you do. Believe me, the ones that run the additive (myself included in that group) see far fewer fuel related problems than those that don't. In fact you'll most likely also see a decrease in fuel consumption when using the additive, which pretty much cancels out the cost for the additive. I know when I first started running it in my service truck several years after we got it, I saw a gain of about 1MPG. Unfortunately I lost everything gained when the ULSD came out, but as least I didn't lose more.
Ultimately, as another post suggested, take the old pump and have it rebuilt and sitting on the shelf for a 'hot standby'. Do this, start running some additive, or possibly a different additive, and your worries should be over for a long while. Good luck.
VE pumps