If, acting reasonably, we consider that our Terms and Conditions have or may have been breached, or that it is necessary in order to prevent or stop any harm or damage to us, to any Jagex Product, to other players or the general public, we may Stop (as defined above) any or all accounts of Jagex Products which we think are connected with the offender subject to such right of appeal as is specified on our website. Such actions may result in loss of membership credit and/or loss of real money paid as part of any item / account trading or other prohibited transaction.
They had reason to believe he had broken the rules, and as such, has breached the terms to which he agreed.
They'll have to tell the evidence to the user. Otherwise the defectness of the product is Jagex's fault and a refund or fixing the product for free is required.
Even if you agree to the terms, the above mentioned laws cancel them.
If you want to argue about the T&C, then I suggest you take up this part. I'm sure they'll be able to answer in a more satisfactory form to you. However, I dare say that it won't help much.
Since I am not banned from the game, I don't really care about this. I'm just trying to help.