I never knew WDTC even OFFERED towncar service to and from resorts.
Any chance you're referring to the free service Disney's Magical Express (DME)? This is a free bus ride (with other people, of course) and free luggage delivery.
We booked town car transportation with our package the first time we went in 2003 (before I realized how much cheaper it could be booking separatly with codes and discounts) and the company was Star taxi and town car. We did not ask about a grocery stop nor did they offer one.