I believe that if you keep good records of the amount you have charged that was paid to DVC for the timeshare ownership, you probably can deduct the interest as mortgage interest. It is not the fact that you are paying interest to a mortgage company, but rather the purpose. He can get a loan from me for all the IRS cares, as long as the proceeds are going to pay for the timeshare, that is what is important.
If you keep good records showing that the charge was to DVC, and keep a record of the interest payments that are specifically for the amount charged by DVC, you should have no problem. If by some chance you are audited, simply show the original charge by DVC, and your records splitting out the amount of interest payments for the DVC portion on your charge card - they most likely won't hassle you any further.
Ask a CPA to be sure - but, I am fairly confident that you don't have to take a loan from DVC or other mortgage company as a pre-requisite for deductability of interest.