Well said.
Also many people confuse copyright with trademarks and vice versa. And some "fan" works do violate copyright. Or trademarks. And in some cases even patents, where the broken law allowed patents on software.
And both copyright and trademarks do have their fair use cases, wich means that there are situations where the right holder can do nothing legally to stop you from doing it. Oh, they can do some non legal things that appear legal. Like frivolously suing you and hoping you are in a situation where you will not go to court. I did mention the broken law systems, did I.
As a rule of thumb, there should be no way in hell anyone can be confused about the creation as coming from the trademark owner. It also helps, if you are not competing in the same market. Those laws are made to protect. If you create brand x and someone makes a cheap knock off brand called k cashing in on similarity, brand owner x can sue copy cat brand k.
Now to put out a hypothetical scenario. You make a parody game of Superman doing homework. Since I do not think that there are any such games out there by the IP owner, I guess there will not be any copyright violations possible, as there is nothing to copy from. Should you trace some comics however, or use screencaptures, you are in fair use territory of copyright and have to figure out, if you are still doing fair use or not. And of course, is there trademark issues ? Is DC in the market of indie parody games? Will the game hurt sales of their own games? Does it damage the brand? Typically I would say no to all three and even claim the contrary for all three. It is free advertisement for them. It increases brand recognition. No one will buy a fan game instead of the real AAA title. This is not some motor oil or softdrink. But, alas, this is legal territory and there is a reason why lawyers and big companies have a bad reputation. So I am stealing that one: (IANAL; TINLA)
Still, I think it is an explanation why there are so many "fan" games out there not taken down. Not only because they do not care, but because in many cases, because the game actually does not violate either copyright, nor trademark.