The show was filmed as if it were a documentary about the government, specifically following the Parks and Recreation team. This is why there are a lot of times where the cast look directly at the camera, to remind us that this is supposed to be us watching them through a camera crew.
With that said, in regards to the censorship, things happen in life, unexpected things. Sometimes, without warning, there's someone walking naked down the street for no apparent reason. When documentaries are filmed, those filming intend to capture everything they can to capture the realness of the situation, whether it's believable that it would happen unscripted or not.
By incorporating adult themes into the show, and censoring them, the show is achieving a couple of things. First, it adds a comedic level, because it's funny to see random things censored on screen when, as an adult, you know it's silly for that particular thing to be censored. Second, it alludes to the fact that this documentary is being shown on some cable channel, making the documentary part of it go a little deeper and allows you to get drawn in a little bit more and invest in the characters.
In short, the censorship parts weren't accidental, they were added to add a comedic level and to add some realism to the show.