I should have said 1080i, not 1080p. My point was, if both television programs (as seen by the viewer) take up so much bandwidth that there is not enough room for the other program to be at "maximum quality," then the other program will not be at "maximum quality" and the earlier editor's claim that channel-sharing (typically) results in a lower maximum-quality show (as displayed on the customer's screen) is true.
Also, of course the two companies must cooperate in a technical sense. I should have clarified that by "cooperate" I meant in a business sense, as in "okay, you want to transmit an HD program from 7-8PM on December 1 and you say that the nature of the program requires that you use minimal compression and you will need at least 15 Mbit/s of the available bandwidth? We already have plans to broadcast a show at 720p during that time slot. We can't both be on at the same time. How about you do your broadcast with some compression from 7-8PM then replay it after midnight with minimal compression when we are off the air?"
If the stations cooperate in this way and the viewer watches both the heavily-compressed and the lightly-compressed version of the 1080i show, there will almost certainly be perceptible differences in quality.
On the other hand, of the stations cannot cooperate, say, because the station that is not doing the 1080i program is airing 720p programming 24x7, then the viewer will be stuck with the lower-quality version.