Chicago Cpap, I'm not a doctor and am certainly no expert on dreams, but I agee with your doctor that a person has most likely been thrown abruptly out of REM if they remember a dream.
Probably that doesn't matter much if it's the last dream of the morning and the alarm clock or house stirring noises wake someone out of the last REM period of the morning.
But if it's happening frequently throughout the night (waking up and remembering a dream or remembering at least the wispy thought of "I was having a dream") I would think that's an indication that the treatment is not yet optimized. REM sleep may very well be being disturbed by apnea and/or hypopnea episodes -- events that are most likely to happen during the total muscle relaxation/paralysis of REM.
While it's fun and interesting to wake up remembering a dream - or disturbing if it was an unpleasant dream - I personally think it's a better sign of treatment going well if we wake up rested and don't remember having dreamed at all. The exception being, as I mentioned before, perhaps remembering the last dream of the last REM period if awakened by an alarm in the morning.
Not remembering dreaming is not the same thing as "not dreaming". I think we probably have to wake up fully for a long enough period (minute or two? 5 minutes? dunno) for the awareness of a dream to commit itself to memory.
We can be dreaming up a storm during much of our sleep and be breathing so well with our machine that we move smoothly in and out of the sleep stages and REM just as Chicago's doctor describes. Sleep peacefully enough and we won't "remember" having dreamed, even though there was a lot of REM and dreaming going on.
Dreaming is good and healthy during sleep.
Remembering the dreams, though (unless last dream of morning sometimes).... I don't know if that's a sign of good treatment.