Minecraft – Are light-level restrictions on spawning different in the Nether

As of the Halloween Update:

You don't have to worry about Zombie Pigmen (they are, after all, neutral mobs until provoked).

Ghasts can safely be kept out by restricting yourself to not using any of the 4x4x4 (or larger!) areas that they need to spawn. Keep a tight ceiling, and you'll be fine.

The answer you are looking for is hidden inside you own question: "there are a lot outside". The game randomly checks places to put mobs and since the outside is much larger than your trap, most of the zombie pigmen spawn there. The mob limit is exhausted pretty much instantly and the game doesn't spawn any more, unless some of the existing mobs de-spawn or get killed.

You will get zombie pigmen to spawn in your trap eventually, but you may have to wait hours for just a few spawns. You need to prevent spawning outside your trap to improve rates of your trap. This is very difficult to do in the nether, since you can't use light or water to prevent spawning. That is why you don't see zombie pigmen traps, building one is a monumental project. Notice for example here a huge area is covered with half-slabs to prevent spawning.

The spawnable area is +/- 8 chunks from each chunk where there is a player (minus the chunks on the edges of that area). If a single player is online, mobs spawn in 240x240 blocks area centered on the player chunk, that is roughly +/- 120 blocks from the player.