That seems like nothing but a goofy way of lampooning how a lot of rich TV characters are given totally generic business backgrounds, but Community went with something a little weirder. You see, Chevy Chase's step-grandfather, Cornelius Vanderbilt Crane, was the heir to the Crane Company, a conglomerate that has, among other interests, a plumbing division. They even gave Pierce's dad the same old-money name of Cornelius, made him resemble a more ridiculous version of the real person, and, uh, wrote him as an abusive racist. Was that based on reality too, or did they kind of screw over a dude who took in Chevy's mother?
Sony Pictures Television, The Crane Family
The episode "Celebrity Pharmacology 212," wherein the gang puts on a lame anti-drug PSA that Pierce ruins/improves with his antics, is also based on Chase's life. Some of the characters dress as bees for their role in the skit, which seems like a random cartoony visual but is actually a reference to the time that Chase got in a fight with Bill Murray backstage on Saturday Night Live and John Belushi broke it up while wearing a bee costume.
Sony Pictures Television
Supposedly, if you watch the relevant SNL episode, you can see Chase come on stage for his monologue in a way that looks like he's being shoved out there by a Belushi who just wants the show to go on. That's not the only SNL reference Community crammed in. When Piece's off-screen death is revealed in "Basic Intergluteal Numismatics," the show is clearly referencing the fact that Chase was banned from hosting SNL for being essentially impossible to work with.