No, it isn't an over simplification. It's an analogy. It's representative of the situation and doesn't preclude your statement regarding inequality of treatment. I can easily point to three campaigns, ranging from $50K to $200K+, for other Star Trek fan productions. These productions are also not one-offs, but rather ongoing series.
I didn't say 'oversimplification'. Just simplification, and in particular one that removes a rather important nuance: RPG companies specifically encourage players to make their own adventures and stories (in addition to hopefully purchasing their company-produced ones) - although with a few exceptions, they don't expect players to publish them from profit. It's not a far cry for players to go from making adventures for their own use to sharing with others, and so RPG companies don't frown on that as long there aren't copyright or trademark violations or implied endorsements.
Television and film companies certainly like for their to be (positive) buzz for their properties, but they don't generally encourage people to make their own stories set in those properties. That said, unless copyright and trademarks are infringed, there's not much they can do against fan fiction besides a stern glare.