Arms and Equipment Guide, pg 95.
Tessellated Armor. With the spoken command word the armor goes from a tiny box in your hand to your body, in one round.
...oh wait, no magic items.
seriously... do what Kell said.
If this guy has it in his head that armor is the worst thing D&D has to offer, have someone play a core-only, full battlefield-control-dedicated conjurer.
See how he feels about ridiculous armor rules after his melee guys lose the fifth straight fight in a row with no save.
Have a malconvoker start planar binding 14 or 15 HD devils at level 10 and have them stand watch. While you're at it ask them if their armor gets uncomfortable.
If you are travelling, standing watch over the camp at night, or anything else with a less than 90% probability of combat, the DM will rule that the armor became so uncomfortable that your character have taken it off.
Like this. No offense to your buddy, but I'm sorry... this is just stupid. The whole point of having someone standing on watch is that your group is expecting some kind of ambush. That person is on guard duty, prepared for combat at any time. Tell him that by his logic castle guards, caravan guards, and the city watch shouldn't be wearing armor either. After all, they aren't expecting combat, right? They're just on watch.
And also let him know that denying characters appropriate WBL totally wrecks the CR system (not that it was good for much in the first place, mind you). A party without their wealth is anywhere from a half to 3 ECL lower than their average character level, if not more.
Now of course I'm not totally against low magic/low wealth games, but in my experience they are hard to do. If you are going to limit magic items for the party, you have to do it for the enemies too, or you will easily kill the party with every other encounter and destroy any suspension of disbelief the players might have about your world. Not to mention spellcasters have to be a rare thing in general, to explain the lack of prevalence of magical things. If you have even one spellcaster in your party he's easily one of the most devastating things this world has ever seen.
You also have to limit the appearance of any type of monster that is "magic related" in any way (possibly to zero), to go along with your lack of magic items and spellcasting in general.
This includes constructs, non-incorporeal undead, magical beasts, dragons, fey, elementals, and outsiders (divine magic is still magic). Also note that without magic to help you, incorporeal undead can also easily lead to a TPK.
And depending on how your world handles the origins of such things, you could possibly have to include oozes, aberrations and things with the shapechanger subtype in that list as well.
Does your DM bother to think things through this far? Or does he simply like to watch his players squirm under what would otherwise be a trivial fight?