Apollo 1 was pumped to a high pressure to make sure it was sealed properly. The partial pressure of oxygen was probably 5 times (or more) than it was in the outside air which is what I'm sure they meant. Combine this with a load of uninsulated wiring and it was kind of inevitable.

The fire wasn't a quick thing though, they were alive for a good few minutes after it started. The problem was, the door of the capsule opened inwards, and so they couldn't open it due to the pressure inside the capsule.