From a technical standpoint, for the same number of users, system speed will actually increase. This is because digital communications systems use a method of handshaking to verify no data was lost in the transmission. When you have low signal strength, the communications system will lose bytes (information) and will request retransmission of the lost information. (Sort of like not hearing someone and asking them to repeat it.) This retransmission takes time and bandwidth away from other tasks (i.e.; other users).
However, from a human side, it is just the opposite. As more folks learn that having a amplifier and better antenna increase their throughput (speed) because there is less repeating of information, they are more likely to use the system instead of finding other solutions (or just not bothering). This increase in users will slow the system.
So the park owner was incorrect from a technical standpoint. But from a from a human sociology point of view, he/she has a point.
Steve
