Most likely you’re meter is telling the truth but you’re misinterpreting the results. A motor winding can be burnt in a way that it still has continuity but can’t carry current.
For example, measure the resistance on an incandescent light bulb. You’ll notice the resistance doesn’t correspond to the wattage. This is because when the filament is actually loaded it turns white hot and it’s resistance goes up tremendously.
For this reason, the best way to check a motor is by doing a loaded circuit test and not an ohmmeter test. You make sure the motor is receiving the proper voltage and then see if it is running or not. If not, it’s bad or out on thermal overload (meaning it’s bad or there is some external problem that needs to be corrected).