They are saying THC because it's in your lungs.
They can assume that because of the pipe found in common infers recent ingestion.If the pipe had been in someones pocket it would have been different.They may have felt you could get it thrown out do to an illegal search.
So this charge won't hinge on the search.
I don't know Wisconsin law but that is a weak argument in any state.Many PD's have changed their misdemeanor marijuana arrest procedures to reduce jail crowding.
Some only write tickets if under a certain amount of grams.
Some PD's give some kind of performance points for an arrest.Not officially called points because quotas are illegal.But it matters in performance evaluations.So police are getting real creative.
Its a misdemeanor so you may not get a court appointed lawyer if your not facing jail time.The police know you will probably end up defending yourself.A decent non-lazy lawyer could most likely beat this.

