You are absolutely correct. I have taught my daughters if they ever need help, call the firemen, not the police. The firemen will be there in less then three minutes, police could take half hour or more. Firemen are experts in first aid and life saving, police are not. Police if they can find a reason will leave you with a ticket or a fine to account for their time.
Exactly correct. You're not paranoid if they really are out to get you. About the only circumstances I could imagine where I would voluntarily call the police would be a burglary or auto theft where I needed a police report to collect my insurance.