Other than not making advanced reservations, why would a guest be considered ineligible for DME? Everyone staying on WDW property should be eligible, except for people staying in the hotels not owned by Disney (Swan, Dolphin, Shades of Green, and Downtown Disney area hotels). If it's those people, then I can understand a bit of why the livery companies are concerned. The DME busses should only go to the authorized Disney-owned resorts. However, the greeters should be allowed to refer guests to the Mears counter if a guest inquires about a shuttle to a non-DME resort. Perhaps they should say something like, "There are many transportation options available for your hotel," and then inform them of the locations for all services at once.
I don't like the idea of DME greeters soliciting, but I question how much actual soliciting is going on. If a passenger hasn't reserved in advance and inquires about taking the shuttle, and the greeter says that they can still use the shuttle, that's not solicitation on the part of DME. If a Dolphin guest inquires about DME and learns that the hotel is not included, then asks where they can purchase a shuttle ticket, and the greeter refers them to Mears, it's not solicitation. If that same person just stands there for a moment, pondering their transportation options and the DME greeter says something like, "If you'd like, you can purchase a ticket to the Mears shuttle," that
is solicitation. I think people in those kinds of positions tend to offer more information than they probably should, in an effort to be helpful. I know I, myself, would be in big trouble that way (future reference librarian: I need to fill information voids). Maybe part of the greeter training needs to include instructions: "answer, do not ask or offer."
