My off-the-hip answer is that your DM is 1/2 right. When you start with a monster straight out of the MM, any increases would already be "built in". Like a troll has 6HD, you don't have a floating "+1" you can add to any stat.
However, if you took levels in monster, you should get that stat increase. When the troll hits 10HD of troll, it should get a +1 to a stat. I think it even goes beyond that, in that it should actually get the increase at 8HD, ie another 2 levels of "troll".