I know nothing about the entertainment industry, but this idea of 'putting in your dues' by working your way up from a menial position based on personal relationships has always seemed naive. Either you can do something or you can't, and working as a dogsbody isn't going to impart those skills. This advice seems like the equivalent of telling someone who wants to be a game programmer to start in the QA department. Yo…
What writers don't understand (and what they'll rarely be told) is that paying your dues is largely a process of disillusionment. To put it kindly, the industry wants sensible, informed writers who understand how TV is made and know how to write scripts that are easy to shoot and suit the medium. To put it less kindly but more accurately, the industry wants cynical, desperate writers who will write whatever cheap nasty dreck pulls in the viewers.
Paying your dues is like a gang initiation, social proof that you're willing to crawl through Albini's trench of shit to get your script into production. Every menial chore that you perform, every late night you pull, every arse that you kiss entrenches you into the industry, further investing you in the payoff of getting commissioned. The longer you've been a dogsbody, the more confident a commissioning editor can be that you won't argue when they bring in a script doctor, when they ask for a few "tweaks", when they decide that a page one rewrite is in order. They know you won't argue over the casting or ask for too much money.
Entertainment is a shit business, don't let anyone tell you otherwise.