Mr. Nix a slam does not require an athlete to be lifted off the mat. When a wrestler forcibly drives an unprotected athlete into the mat he is subject to the slam rule. Most often we find this when a wrestler has elevated the opponent off the mat, however the same effect can happen with a simple bar from the knees. If you think it's a slam it's probably a slam whether called by the official or not.
Rule 7 Sec. 1 Art. 1
A
SLAM is
lifting and returning an opponent to the mat with unnecessary force. This infraction may be committed by a contestant in with the top or bottom position on the mat, as well as during a takedown. A slam shall be called without hesitation.
Make sure your not giving anyone any false information. Your example of a simple arm bar from the knee's and planting your opponent back into the mat would be considered unnecessary roughness, but more times than not a ref would let that go.
Just because you think it is a slam does not mean it is one whether the official called it or not.