A couple of points that might illuminate this discussion a bit:
1) In the typical dispatch system (including Chelsea's) that uses a voted repeated system, the dispatch console listens to the input frequency of a repeated channel. Subscribers generally cannot communicate with dispatch on "direct" because a subscriber on "direct" is transmitting on the output frequency.
2) While it is possible to enable "direct" reception by a dispatcher, it is complicated. You need an additional receiver (programmed for the output frequency) and an additional channel card, and you also need a way of muting this receiver whenever the console transmits over the system (to avoid the "direct" receiver from hearing the console operator's transmission and generating a cascade noise). As of when the Chelsea UHF system was installed, they did not have "direct" receive capacity at the console.
3) Where a department operates on more than one channel, under usual circumstances the dispatcher will "select" one channel and received audio on that channel comes over the left hand speaker, while the right hand speaker produces mixed audio on all the other ("unselected") channels. So it is not uncommon for a dispatcher to speak to a subscriber on one of the channels, have the subscriber respond on one of the other channels, and unless the dispatcher is watching the busy lights, he may not even be aware of this. Moreover, so long as the substance of the traffic is only between this subscriber and the dispatcher (such as a radio check), the fact that other subscribers hear only one side of the discourse is immaterial.