Even if it was all private Disney still couldn’t just prohibit access.
If it hadn't been a public road, it wouldn't' have provided access in the same way. It would have created a super huge access easement on private property. Disney would have argued that a different route would have given more direct access to a public road. This is the scenario where RCID never existed at all and the entire area was one big private property. It might have turned out the same way, the Bonnet Creek parcel is locked in by the interstate and drainage canals.
If I look at a map today, there's some land East of Aldford Dr and West of Legado Dr, South toward Maple Rd, all outside the district. There's a drainage canal along the district boundary. If we pretend the canal doesn't exist to make this easier, and then pretend someone acquires that a chunk of land there, where there are currently no access roads. That land would need to find access to one of Aldford Dr, Legado Dr, Maple Rd, Floridian Pl, Seidel Rd, maybe all the way to Reams Rd. In this fiction, that person could argue the most efficient access it to Maple Rd, right next to the fireworks buildings. They would likely get pushback that one of the other options is better. The houses on both Aldford Dr and Legado Dr would likely argue that it would add to much traffic. The developer might argue that Seidel Rd and Reams Rd are to far away. There would be lots of options for a court to evaluate and determine which one solves the access problem. In this pretend example, I would bet that Floridian Pl is where access would end up. All the parties arguing that a different "not past me" route is better is not nefarious.
Back to the Bonnet Creek case. The evaluations on the least impactful way to provide access to the disconnected property would have been evaluating entirely different criteria if RCID never existed. That RCID did exist, and that because of that, all the RCID roads are public roads clearly had an impact on the evaluation. One that after it was solved, it looks like RCID has been cooperating with Bonnet Creek on issues ever since, presumably mostly on stuff that impacts both of them, like that drainage canal that runs between them.