I'm dead certain that a lack of productivity and a major fuck up on whatever paperwork he had to do was the reason they fired him.
As for him telling the story, Phil really should've just never mentioned it, because as soon as it was discovered that his dad got him the job, there was no such thing as spinning it in a positive way. Especially since it was the last time he was gainfully employed, and has had to rely on the internet ever since then. And I mean it when I say "had to". Phil is way too dumb to make it as anything but a joke.