Not the finest bit of writing I've seen on the show.
However, as a follower of the research literature on "public service motivation" (see James Perry at Univ. Indiana), I have to say that we often overestimate how generalized the call to serve is across the public service. The noble motives that propel some folks towards government jobs do not propel everybody. And if you run into a low-level clerk at a service counter who is providing anything BUT service, there is a pretty good chance they sought out government work, not because they were motivated by "the call to serve", but by the fact that this was an employer that paid well, wasn't going to leave town, provided some degree of job security, and likely had the sorts of collective agreements that folks in the private sector in similar jobs can only daydream about. Should they be expected to be more civic-minded than the person putting price-stickers on the marked-down canned goods in the pet-food aisle? Personally, I wouldn't think so.
At the same time, I can understand why some here found the rather generic label of "public employee" (which would include your kid's teachers, public health officials, firefighters and police, social workers, and so many more whose motives we do not dispute) a little too broad a brush, given that the skit focussed on one small segment.
As they would say on SNL...."Ooooh-whee, what's up with that?"