It could also be called boldly biting the hand that feeds them. Late night talk shows don't count as they often do this. And this thread is also not for stars/producers who have said something critical off the show, the show itself should be saying it during the show.

Boy Meets World complained about being moved an hour later to 9:30, the kid Cory was babysitting couldn't watch his show anymore because it was past his bedtime.

Grace Under Fire- After Disney's takeover of ABC, Grace very sarcastically quipped We're all one big happy family now.

Back in the late 1970's when NBC was dead last in the ratings, Johnny Carson would make fun of the network a lot for their incompetance. This was back when the only money making shows were Tonight and the Today Show. vCarson was probably irritated of the network not drawing in viewers to see his show. His numbers were already very high but there is always room for improvement.

John Oliver of Last Week Tonight which airs on Sunday makes fun of HBO and HBO's parent company. I guess like Carson, Oliver can present his ire as sarcasm because he is safe in his show and position

What about Simpsons and Fox?

I don’t have the memory to give specific examples, but definitely 30 Rock.

The Pilot arc on Seinfeld poked jabs at NBC.

Married...With Children
In one episode they said, "let's get into our Fox viewing positions" and they all got antennas with aluminum foil wrapped around them!

TV Tropes has an entire list (https://tvtropes.org/pmwiki/pmwiki.php/BitingTheHandHumor/LiveActionTV) of this.