If someone asks at the resort, a wheelchair will be provided, IF one is available. The guest can't be asked to prove a disability when getting one, but Disney doesn't make it easy to know they are available and doesn't guarantee anything.
Disney does NOT advertise OR MENTION anywhere that they have them available and says this on their website:
Disney Featured Providers
In addition to wheelchair rentals locations throughout Walt Disney World Resort, several private companies in the local area also offer wheelchair rentals, as well as
ECVs, strollers and other mobility product length-of-stay rentals.
ScooterBug: (800) 726-8284
CARE
Scooter Rentals: (800) 741-2282
Buena Vista Scooter Rentals: (866) 484-4797
Best Price Mobility: (866) 866-3434
Apple Scooter: (800) 701-1971
That, plus the facts that there is no way to check on availability ahead of time, no way to reserve one and no guarantee there will be any is why people say they are meant for things that come up unexpectedly.
Guests who know ahead of time that they need one would be much better off renting from offsite - doing that, they know they will have one, can specify the size they need and will get one in good condition. That saves the resort wheelchairs for people who may need one right away because of an injury or illness.