They do NOT guarantee any particular rental agency with "name your own price" rentals.
You should note that Priceline deals with several offsite rental companies that require a shuttle (Sixt, Payless, Ace).
The offsite agencies are typically the rental lowest cost option, therefore a very low per day bid may result in one of these companies being selected.
If you really don't want a shuttle, book with an onsite rental agency directly (
Alamo, National,
Budget,
Avis, Dollar, Hertz, Thrifty).
There is probably a thread already running in this forum for the month that you are looking to rent.
Check that thread for rental codes that you may be eligible for and you will get a great rate without the worry.