I honestly think the OP is putting way too much emotion in this. This would also explain the combative attitude towards this board. In the end the OP is not right. Hilton can close the account, period.. tough luck..
The only thing you can do is appeal to reason. Send a simple letter.. maybe something like the below, remain factual.
Dear Hilton,
On the <insert transaction date> i have purchased <insert number> Honors points at a value of <insert price> for my Honors account. I have made another transaction on <insert transaction date> for <insert number> Honors points at a value of <insert price>.
On the <insert date> I was informed of the closure of my Honors account for supposed fraudulent transaction(s). I am not aware of any fraudulent activity in my account and have not received a detailed explanation from your side or a chance to discuss on the phone this perceived issue to clarify why a transaction was made to prevent closure.
I am aware of the option by Hilton to close the account as per the program terms and conditions, this is not a concern where points are awarded at no cost as loyalty benefit. In this case however I have purchased points at a direct cost and am not able to enjoy the intended use because if this account closure by Hilton. Unless the account is re-instated I would require the financial transactions to be cancelled and the funds to be returned to my credit card.
If there is no response or a negative response, take your losses and move on. There is no other action you can take.
Globalist