No experience with playing brass instruments, but I spent six years in school bands learning to play a woodwind instrument (alas, that was way too many years ago). I also "experimented" with a few other musical instruments.
In my very INexperienced and INexpert opinion, the material used does make a difference to sound/tone. As cosine noted, I think resonance may be an issue. I also think that to most non-musicians (myself included!) the difference may be negligible
If I recall correctly, even different metals produce different sounds, and as an example, take the flute. I believe the head of the flute is commonly made of sterling silver for superior tone, whereas the body may include other metals because of cost. Also, I think that the better flutes have "open holes" in some of the keys, again for better sound.
I also recall that there are differences in the sound of pianos. As my piano teacher once told me, old pianos in which the wood has "dried out," will have a "brighter," somewhat harsher sound signature than new pianos. I also remember trying both less expensive (unknown brand) and more expensive (known brand) upright pianos, and there was a difference.
I have to say that plastic musical instruments/parts just don't seem "right" to me. It reminds me of toy instruments, but I'm sure technology has changed tremendously since my day and so plastic is nothing to thumb my nose at.
As an analogy, I see it sort of like plastic flashlights versus metal flashlights. Nothing wrong with plastic flashlights (I love my UKEs and Princeton Tec lights), but metal just seems "better"... So maybe its just a matter of perception.
All of the above aside, I have to say that I'm a little surprised that at your son's age, the music teacher is being so strict. Of course as first chair, he may be tapped to do trumpet solos, and so the teacher may be more critical about the sound.
Just a very UNinformed opinion that should be considered accordingly...if at all.
