According to the Terms and Conditions in the Magical Express booklet that's mailed several weeks before travel, Disney provides exactly the same liability for loss or damage as the airlines. In fact, the paragraph even starts off, "Consistent with airline baggage policies, Disney's liability for loss or damage..." In other words, if luggage is lost or damaged, the Magical Express passenger files a claim with Disney, not with the airline. How Disney works things out with the airline (including who ultimately pays the claim) might make a difference to the shareholders of Disney, but not to the Magical Express passenger.
However, Disney also states that Magical Express baggage transfers are only for Magical Express passengers. Here's what Disney's current policy is regarding DME luggage delivery without riding on the DME motorcoach on Disney's official "
Complimentary Airport Transportation Service - Disney's Magical Express Transportation" page:
Please note that you cannot reserve the luggage service exclusively. You must be present on the motorcoach to have your luggage transported to a Walt Disney World hotel.
Despite this, some arriving guests have apparently been successful using Magical Express baggage transfers without using the passenger transportation.
The open question is whether Disney will still accept responsibility for baggage issues for those who pile into a rental car instead of riding to WDW on a DME motorcoach.