Any 1st year lawyer will tell you to never speak to police unless your lawyer is present but most US citizens still have the idea that speaking with police might help. That is not the way police operate now days.
As to the plate, maybe they had a partial and matched it to a sort of similar car then ran with that instead of actually doing their jobs?
Having watched 1000's of cases now, I am of the opinion that a very significant potion of police misconduct originates with laziness on the part of the officers.
Mark I know my rights but will probably get beat for exercising then where I live.