Oh yeah, depending on how they show up, they're a problem. I'm just saying that there are certain non-problematic cases where only a free parameter will do.

I think the trouble with dark-matter-as-WIMPs is that the free parameter (the location of those WIMPs) is overpowered:

You can say that the extra gravitation is caused by the presence of these particles and leave the details of how those particles got where they are out of your theory. But then when you add "oh, and they can't be detected by any other means" it becomes a problematic free parameter because wait a second, that's the very problem we were trying to solve in the first place. If you can't connect the causal agent to anything besides the problem that necessitated it, then it might as well be a ghost.