They have not stated its being closed due to this. They are not stating anything. I also don't understand how the refund due to removal of services is related to any potential breach of the T & C in any event ... is this a fine for being naughty?
They could, for example, cancel your or my accounts tomorrow, with no reason and no refund and we'd be in the same position.
Essentially, people can write anything they like in a T & C document. It gives you a heads-up on where they are coming from but isn't automatically legal. Companies make this mistake all the time, thinking their word is law, but its really not the case. Likewise, many consumer rights cannot be waived, even by consumers themselves in full knowledge of what they are doing ... its simply illegal to do so.
Proof is so very important though. It really is.
In effect, it appears it's withdrawal of service and a fine for being naughty. It's pathetic that they haven't disclosed the reasons, but all banks are the same in that regard. To further elaborate on this, all loan contracts with all banks include a clause saying they can withdraw the loans at any time, at the bank's discretion, without reason - if you have a home loan (or credit card, business loan, or any other loan), have a close look at the loan documents! In practice, banks do not do this except in exceptional circumstances, as they are in the business of making money from loans. But it can happen, as MAX_1 has found out.
You are correct in that anything can be written in the t&c's, but that doesn't make them legal and t&c's cannot take away statutory rights, however I doubt that would the case in the situation we are discussing, where the cardholder has admitted the card has almost, if not, entirely been used in breach of the t&c's.
I agree that proof is very important, which is what I rely on when I rent a car and breach the conditions! In respect of the the situation we are discussing, I don't think it would be hard for HSBC to prove the card was being used for business use, in breach of the t&c's.
EDIT: IME, the point here is still that the t&c's (prohibiting business use, which, whilst I don't fully understand, I don't think is unreasonable per se) were deliberately breached by the OP's own admission. Aside from the fact that HSBC didn't disclose this as the reason, is reasonable grounds to withdraw the service.