However when you invite the public into a space even if they have to pay the space then becomes public for the period of time the public has access to it.
It's not that simple though, especially if we go back to this....
Any member of the public can film or take pictures in any public space they like and they don't need anybodies permission to do so.
....again, not as simple as made out.
If you are on private property, regardless of whether you believe it to be a public space or not, you can be asked not to take pictures and you are obligated to honour the request.
The employer of Flamingo and 455driver are telling employees as a company rule that they cannot stop people taking photos, it's not because they wouldn't be allowed to do so from a legal standpoint.