The terms and conditions document item 10 requires prior written consent of the university to make alterations. Item 21 says that they may "declare a material breach of the agreement and elect to terminate the agreement and remove the student" if "The student causes material, substantial, or continuing breach of the agreement", and note that "If termination is sought by the university, the student will have the obligation for all past and future amounts owed under the agreement".
In the Housing Agreement document, it states that "Beds can only be elevated on supports provided by housing" -- this could be interpreted to mean "only on a specific 'support' supplied by housing for this purpose" or, "only some object that could support the bed as long as it is is supplied by housing". It's hard to imagine a judge or jury that would think that the latter is what the clause says. It also says that you can rearrange furniture "as long as the arrangement is deemed safe by your hall advisor". Now, payment of a fee will not change the safety of the rearrangement, but it does indicate another way that you could be in breach. Finally, under fire regulations, they state that "Any violators will be disciplined on the first offense, and could be asked to leave housing". Again, if the stacking is a violation of fire regulations, then you would be in breach, though a fee does not mitigate the violation.
I assume that the contract that you actually signed states that all of the rules are contained in "Terms and Conditions", in which case I think you are right that there is no provision in the contract that allows them to forgive these possible breaches, in exchange for money. One can, of course, ask the relevant authorities what the legal basis for this fee is, but a possible answer would be "You're right: get out". My hunch is that safety and fire considerations are foremost in their concerns.