In the link you posted it explains how it does not change your test result or interfere with the test when you read seachems response. Like I mentioned prime only locked up the ammonia so it is not toxic, it does not actually get rid of it. In doing so our kits measure total ammonia, not just toxic, so you get a reading that is the same as before you dosed but it is now inert and can not harm the fish. You do not know from a simple test kit how much is inert and how much is toxic which is why you need to dose according to directions.
As far as bottled snake oil, I am simply sharing my experience. My lfs used to get it in on ice, it was not frozen just the dry ice kept the coolers cold so it arrived at a refrigerated temp and then it was placed at the store from the cooler right into the fridge for sale. When they did that it worked the one time I used it. Since they changed I tried it multiple times with no luck. I do not believe in overnight cycles, maybe they help shorten it from 6 weeks to 5 or 5 to 4 but there are too many variables that I never tested for to say scientifically it does not work, just seems I still had a normal cycle even with it's use. Only thing that worked 100% of the time to shorten a cycle or jumpstart a stalled cycle for me is taking media from an established tank and putting it in mine, whether it be live rock, sand, or sponge filter.