LOL - Their information is vague enough that I suspect that, while they do "suggest" that they have some sort of special access to the Beach House, they are referring to the public beach access available at the property - where anyone with Palmetto Dunes access can park at the Beach House lot (even under the building itself), can use the public restrooms there, can purchase food at the snack bar (there is a walk-up window outside for the public), can use the public grills next to the Beach House and can use the beach in front of the Beach House.
Since they don't specify any details about the "certain privileges" at the Beach House, I'm 100% confident they have no sort of real access to the pool or other facilities accessed only by room id into the building. They are using the public access available to everyone within Palmetto Dunes to try to improve their rental opportunity.
The only thing they don't have access to is the inside of the Beach House!