Since we're discussing the time checks made by the dispatcher, then what's relevant are the two clocks in the dispatching room.
What does "generally reliable time" even mean? And if you could "hardly see it" then how could it have been used to synchronize the others? And what was that clock synchronized to in order to make it "generally reliable"?
I think all this mess shows is that the time checks given by the dispatcher are unreliable, and the preponderance of the evidence is that Tippit was shot earlier than the official narrative wants it to have happened.
Back in the era of the assassination, if I wanted to know what time it was (in order to set my wristwatch for example) I would most likely dial a certain number on the phone and an automated voice would give me the time by saying “at the sound of the tone it will be...”
Now, was this the official standard time? No, it was the time that the phone company said it was. But it was close enough to the standard time for the vast majority of people. We assumed that the phone company synchronized with the official government time often enough so that their time stayed very close to the official time.
“Generally reliable time,” in the context of Bowles’ statement, simply means that that particular clock stayed in sync with the official time for longer periods of time than the other clocks he mentioned.
Much like it was reasonable to assume that the phone company kept their time closely synchronized with the official time, it is reasonable to assume that the DPD kept their time synchronized with the official time also. (Otherwise, Bowles wouldn’t have known that one clock was generally reliable).
Just because it was not the most visible clock does not preclude them from using it for syncing.