Then it may still the starter motor, even though it tested okay. What happens sometimes is a bad spot on the commutator lines up with the brushes and the starter won’t turn over. If it gets bumped, wiggled, or jarred enough by the solenoid (or by removing it from the car) to move to the next segment, it will turn over.
Here’s an article on starter testing. You may need to open the starter up and see what the brushes and commutator look like.
http://www.misterfixit.com/starttst.htm