State laws vary but yes, in most states you would be in violation of the law if you drive a vehicle that does not have at least the state required minimum insurance on it by the car owner. Most states require valid car insurance to be on a vehicle in order for the registration to be valid so if a person's car is uninsured it may have had its registration suspended and thus you could be cited for driving without insurance and suspended registration.
While you may have insurance that covers you operating your vehicle, and that may extend to be secondary insurance while driving other vehicles, that insurance coverage would not normally extend to be primary insurance on other vehicles that you drive that are not listed on your policy. When driving a car the car owner's insurance is primary with the driver's insurance, if different than the car owner's, being secondary. This basically means if the car owner's insurance policy's Liability limits are exceeded your Liability coverage from your policy may be able to be used.
So your car insurance would not cover an uninsured car normally. You would likely be cited for driving without insurance by law enforcement and showing them an insurance card for a different, insured, vehicle would not stop police from writing you a ticket since you need to have the car you are driving listed on the insurance card to count as proof of insurance.
If you need to buy insurance so that all the vehicles you drive are covered by auto insurance you can click here to get instant car insurance quotes.