First there is no "Fair Debt Act". There is the Fair Debt Collection Practices Act(FDCPA), but that only applies to 3rd Party Collection Agencies and not Original Creditors(which RAC is).
There is no law that you have to be 30 days late before they contact you. In fact there is nothing that says they can't call you for being even one day late, or even calling you ON or BEFORE the due date. You have to remember that you made an agreement that said you would pay a certain amount on a certain date. In return for that agreement you have a (insert item leased).
As you found the best way to make the calls stop is to pay them, or return the item.
I really do hope that you follow your own advise for the future especially this part..."or figure out another way to get what I need"
All Rent-To-Own companies have extremely high interest, and saving the money in advance and then being able to go into a regular store will save you a lot of money in the long run.