Based on the available information (and I'm sure there is more information that has not been published due confidentiality as the result of a settlement), there is virtually no likelihood that the petitioner would have succeeded. If the ADA could be boiled down to two key words, those words would be reasonable accommodation.
Individuals that fall within the purview the act are not permitted to specific accommodation of choice, but simply accommodation that is reasonable. One can analogize this to the 6th Amendment's right to counsel. That does not mean a defendant in a criminal proceeding can choose any lawyer that he wants at the expense of the state; it only requires that the state furnish him with competent counsel. Individuals with disabilities cannot insist that they be allowed to drive Hummers within the parks. Disney just needs to ensure that there is a reasonable accommodation in place.
If the petitioners in this situation had a strong claim, there are plenty of groups out there that would have advocated on their behalf - not wanting a settlement in order that they can set precedent for others in the community. Those groups probably chose not to step in and force the issue because it was a loosing battle. (Note that, had the petitioner lost in the form of a court judgment, that would have actually created a negative precedent for individuals with disabilities.)
This is why settlements are viewed as the only win-win alternative dispute resolution. It is often said that, in court, no one really "wins."