NyQuil's scientific advisors are not doing their jobs. Or, more likely, don't exist.
Is it a little petty to go after NyQuil for an obvious joke that just happens to be of questionable scientific merit? Maybe. But then again, there are about a hundred other ways the joke could have been written that wouldn't have violated the fact that roosters' crowing is not based on simply seeing the sun. What's wrong with just saying "...before we got the rooster" or "...before the rooster moved into the bedroom" (as it apparently has)? Of course, I'm going to go out on a limb and guess that the people who made this ad think that roosters crow because they see the sun; it seems like a common bit of folk wisdom even though thinking about it for more than ten seconds should be enough to make anyone realize that it doesn't make a ton of sense (and if you actually own a farm, chances are you've noticed that roosters crow at various times, for various reasons).
The thing that always gets me about NyQuil ads is the way they kind of tiptoe around the fact that the main purpose of NyQuil is to knock your ass out. It'll be the best sleep you ever got with a cold because once the drug that's five times as powerful as morphine gets in your system, you'll be lucky if you don't wake up covered in your own urine. I'm not sure why they bother dancing around this as though it's not totally common knowledge at this point. No one's taking NyQuil and trying to go to work immediately after. Except perhaps for the people who made this ad.