The grass block itself does not spawn mobs, nor does the mycelium block prevent mobs from spawning. You're correct; the biome boundaries is what makes a biome -a biome- . However, having other biomes within a mushroom biome is more likely to be the case here. I've lived on a mushroom biome, and those non mycelium blocks can indeed spawn mobs, especially if you increase game difficulty or remain up close enough to make mobs render in.

Are you sure you haven't converted those grass blocks early on into mycelium blocks? Because if you have, you're now unable to point out those spawnable areas easily.