I know of no state or federal laws that control how home owner's associations bill their members. Accordingly, the HOA's rules and bylaws will control. If the rules are silent on this issue then common sense applies.
My guess -- note my word choice -- is that the HOA wants you to provide it evidence of the ownership of the property so that it can go to that party with the evidence you provided in-hand and show the owner that it owes the HOA the quarterly fees. In other words, the HOA wants you to do its homework, which is a reasonable request in my humble opinion.
I hope this information helps you Find. Learn & Save.