Kind of like the way murder suspects in police interrogations might give unprompted and quite possibly fake confessions to minor crimes, to manipulate the police into believing the suspect is being open about everything and doesn't have anything to hide.
Part of my doubt stems from my confusion about how a traceless dart gun would actually work. The dart guns I know of fire darts with fletchings, they can't be discrete. If you removed the fletchings, the darts would almost certainly tumble. If they said it was a BB gun that fired poisoned BBs then I wouldn't think twice about it, but they say it shot darts..