The regs allow Disney or any public accomodation to ask for the presentation of a valid state issued disability placard, they even add that if the placard has expired than it is not valid. Most people who know that that is the rule will be prepared and comply.
Lets assume there is a shady rental company that tells their patrons to lie about how long they have used a Segway. If their customer has an accident and Disney discovers that the company is telling their customers to lie, what do you think Disney's legal Dept will do to that company? A reasonable rental company will want to independently verify that their customer has a valid disability placard and has sufficent experience to use the machine safely at Disney prior to renting a machine outside a Disney venue. The rental company absolutely could have a prerequisite of a presentation of a valid state disabled placard to rent their machines for use within Disney.
Disney has plenty of security that knows how to eject someone acting recklessly within their parks.
I doubt that you will find people checking for proof of disability before renting the Segways. In fact, if the person needs it for a disability, it would be illegal to ask for proof of a disability, just like Disney cannot ask for proof of a disability before renting out an ECV or wheelchair. And a disability placard does not mean anything other than the person cannot walk more than 200 feet without some kind of assistance or is blind etc... I had a wheelchair for months before getting my disability placard. Some people do not have one because they live in cities and do not drive, etc.
Asking if a person has experience with a Segway is perfectly legal and SHOULD be asked. I doubt, however, that many companies will. I am guessing that many companies that already rent wheelchairs and ECVs will just add Segways to their websites...