First registered/posted in 2011, and you just noticed this problem. I don't think so!
This is another made-up post from those at Pianostreet who refuse to formally recognize and feature the piano technique experts of our time (Taubman, Golandsky, Mark).
Are you for real?
@OP I don't like the use of the word relaxation in terms of piano technique because it creates the kind of misunderstanding that you are demonstrating in your post. Yes, if we relaxed completely we would fall of the chair, but we can still have a completely soft and supple arm while we play. So it's not "okay" to still have some tension in the arm. (Don't misunderstand me, of course it is okay to struggle with relaxation, but the goal is the complete freedom of every joint in the hand, arm, and shoulder).
I.e. the goal for your "relaxation" work still has to be that whenever you play any note, any chord, any type of passage, before, during, and after pressing down any key with any finger, your wrist should be so loose that somebody else (or yourself) could grab it and push it in any direction without feeling any resistance or stiffness from your body.
I have found over the years that forearm tension either comes from putting pressure on the fingers with the strong muscles higher up in the arm, so you have to tense up the forearm (where the muscles that govern the wrist and fingers are) in order to resist the pressure (else everything would just collapse under the pressure), or from trying to inhibit yourself and "holding up" things. You might for example constantly hold your elbows up instead of letting them hang loosely by your side. Or you might subtly try to "hold up" your fingers, away from the keyboard, while pressing down the keys, so that you are not firmly holding down the keys in the keybed, but your contact with the instrument is flimsy and insecure. This kind of inactivity in the fingers causes you to use the arm instead to prod down the keys, which creates a similar kind of problem as if you are pressing down on your fingers as described above.
Are you able to completely relax your arms and hands, then rest the hands in a natural playing position on the keys, while still keeping finger, wrist, elbow, and shoulder joints relaxed, and then play a key by moving any finger? Feel it as if the movement is originating from the fingertip, and make sure everything else remains loose. Make sure the movement is only with the finger, and that there is no additional pressure from the hand and forearm, or that you are not tensing up and inhibiting the arm from being able to move!