Yes, strong opinion here. I don't understand what problem they could cause. Was there an explanation? The screen keeps animals from entering and causing problems. Hornets may also build nests in there, even with the screen in, but the screen is removable to get the little buggers out. Inducer motors and piping don't like dead birds and their nests. Determined rodents can climb or jump into and exhaust pipe when fleeing a predator or looking for warmth.
Also, there is the human-factor. I have taken a variety of balls out of pipes and motors that have no screen. Kids are curious and put balls in pipes. Go figure.
If he is worried about flow resistance causing an air switch to trip, then his concern should be directed more to the number and type of fittings used for the vent.
The screen should never be installed on the interior hub of the last fitting and glued in.
Otherwise, I still don't know of any problems that a screen could cause.
Please ask and let us know. Maybe he has a secret that the plumbing world should be aware of.