I've seen this commonly with new fan fic writers and sadly, teenagers. It's very rare that I see anyone over the legal drinking age, we'll say, just randomly throw something together that can be done with any character anywhere.
On these forums, I've yet to see that, but then again it's not like I've read through every single fic here, but the ones I have read, I think have been done with your basic understanding and concepts of grammar, a good imagination, and a good dose of knowing your Muppets!
I understand what you mean (I hope) - it's when you get an idea and instead of tailoring it a particular fandom (in our case, the Muppets), a writer will just insert character A with like character B and go from there and you're right, that is the lazy man's way of writing.
While the Internet has opened the door for many people who wanted to try their hand at writing or are writers that never got published, it's also become a form where everyone thinks they're a writer, when - sorry to say - they aren't. Or perhaps it's that they don't understand that writing actually takes time and thought.
It's one of the reasons I turned to fan fiction in the first place - my original works get started and then take years because I'm working out characters, situations, character bios, family ties, etc. I'm still working on the two series that I started way back in junior high!
Ideas are easy to come by, but being able to put people in the right places and vice versa is important. It's like the idea of another actor portraying a certain character if things had gone differently; ie, can anyone see Sean Connery as Gandalf? Or if roles are reversed, not for the purpose of a story per se (like a Freaky Friday-esque plot line), like Fozzie acting like Gonzo or Kermit and Piggy not being a couple (just for the sake of them not being a couple)
The unfortunate thing I think is that many of these writers just don't care or are under the impression that we as the reader have no right to tell them how to write or engage us; that's primarily why I no longer post or read anything on fanfiction.net (though I do get alerts for stories and/or authors that I enjoy, but that's a few). I've had enough 'youngin's' decry the very audacity that I would suggest something for them to consider. I've even gotten called out on it and acquired my very own troll stalker because of it (It's also why I don't review anymore).
Now with all of that said, I can see writers having a hard time with say, a particular character. But, this is where doing the research (which many fic writers do not do) is key and paramount; I don't ever accept the excuse that a person doesn't know about a particular character when we live in a world of YouTube, Wikipedia, and Bit Torrent. Unless something is so obscure or a character a passing glance in something, there is no reason that a writer can't sit down and try to learn about a character.
But as I mentioned, many don't for whatever reason and then we get character A doing something with characters B, C, and D and hilarity may sometimes ensue.