They're not trying to publicize vampires and demons but they're not trying to hide them either. Their lies seem more focused on not being arrested or declared insane, rather than fool anyone. The supernatural has enough people who pay attention to it, that there are inherent checks and balances. Slayers being one of the major checks on various supernaturals.

They may just want to ensure that the SGC realizes that they are accountable to someone. They don't have complete free reign to do what they want.

It would be a good story but I have too many stories in the works already. I'll give this one a pass.