As a Florida native, who grew up with hurricanes and moved from Miami just months before Hurricane Andrew, I do not agree with your statement about Disney being so far inland. Being in the middle of the state helps, but the Florida Peninsula is not wide enough, nor does it have enough undulating terrain to protect the center part of the state if a large Category 4 or 5 storms makes a direct impact into the coast. Disney will not have to deal with storm surge which causes a lot of damage from hurricanes, but sustained high winds and tornadoes near the hurricane eye can impact almost anywhere. For an east to west or west to east moving storm, the State of Florida will slow the storm down, but it will likely traverse the entire state as a hurricane and strengthen upon exiting into he Gulf or Atlantic. The island of Cuba actually does a better job of degrading a storm because of its mountain ranges.
I think a lot of policies have changed at Disney in the last 20 years with regards to security and those impact the decision to close the park. This has been more evident over the last 5 years as Disney has made vast security changes to likely known threats Disney has not disclosed. Disney relies on the Orange County Sheriffs department to show a large police presence, and the possibility of any level hurricane or tropical storm will cause Orange County to shift efforts. Tourism revenues are a major priority of Orange County, but the safety of residents takes priority.
A few examples I found online from 1995 and 2004 are below. Disney closed the parks for portions of the day, but I would guess similar examples today, would have caused the parks to close for the entire day. A lot has changed with Disney's Security posture and procedures that weigh in the decision to close the parks. Just look at the expanding secure zone, as Disney continues to reshape their park entrances and push the security checkpoints further and further away from the park gates.
"Back in 1995, category 1 Hurricane Erin hit Walt Disney World in the early morning hours, delaying the park opening until 11AM. Though the rain from the storm continued throughout the day, the weather wasn't severe enough to impact regular operation, and even though some attractions were closed, most guests enjoyed what they could on a very soggy day.
While this example saw the park opening early, Walt Disney World may also elect to close its parks ahead of schedule as well. In 2004 during Hurricane Charley, all parks were closed by 1PM the day before the hurricane was scheduled to hit in order to prepare for the imminent category 4 storm."