The State and their oppressive gator hunting laws also plays a role in this.
To catch nuisance gators in FL isn't as simple as calling Animal Control. You have to go through a licensed gator catcher (not sure the actual term) and that person needs to apply for a permit to hunt a SPECIFIC gator.
Failure to do so can lead to very steep fines and even jail time for those in breach of the law.
68A-25.003 Taking and Disposal of Nuisance Alligators Statewide.
(1) Only persons under contract with the Commission as nuisance alligator trappers, or their agents and assistants, who have been approved by the executive director, or his designee, shall take, possess and kill nuisance alligators as authorized by permit.
(2) Persons may apply for nuisance alligator contracts by completing and submitting a Nuisance Alligator Trapper Application (FWC Form 1002AT (2-06), incorporated by reference herein).
(3) Five dollars ($5) shall be expended by the Commission or its designee on marketing and education for each CITES tag used under the provisions of this rule contingent upon an annual appropriation by the legislature for marketing and education activities. Rulemaking Authority Art. IV, Sec. 9, Fla. Const. Law Implemented Art. IV, Sec. 9, Fla. Const., 379.3012, 379.3751 FS. History–New 8-1-79, Amended 10-23-79, 6-22-80, 6-4-81, 6-21-82, 7-1-85, Formerly 39-25.03, Amended 6-1-86, 12-23-87, 5-5-88, 2-14-89, 4-11-90, 4-14-92, 3-30-95, 4-1-96, Formerly 39-25.003, Amended 4-30-00, 12-16-03, 5-18-06, 8-19-14
Here's the whole law:
http://myfwc.com/media/1531908/alligator-rules-booklet.pdf
So, the point is, it's not as simple as having someone on property at all times to deal with nuisance gators. First, that person must be approved by the state, and second, the person much apply for a contract on said alligator (and also proving the gator is a nuisance) to be approved by the state before they can go after the gator.
Apparently this gator (or another one?) lunged at some Brits staying at Poly a few weeks ago...but, even if that's the case and Disney was notified and aware (before it was reported to the Telegraph, who broke that story), and they contacted a gator catcher, they'd still need to wait on the state approval of the "contract" before the catcher could get to work.