Sorry, but this "myth" has proven true for me for the past 30 or so years. A cycled tank is one that will immediately cycle ammonia through to nitrate; I am not suggesting that the capacity to do so is unlimited; it's obvious that the capacity to do so is limited by the total amount of bacteria transferred by this practice. I always keep an extra sponge filter in most of my tanks, so when I set up a new one and utilize one of these filters I am only gaining the capacity of the bacteria on that filter...which is naturally a fraction of the total bacterial population of the original established tank. Typically, the original tank won't even show a blip in ammonia, although in a tank that is more crowded than mine tend to be, a "mini-spike" is certainly possible.
The new tank now has a significant bacterial population, and that population includes those utililzing ammonia and also nitrite; this alone is a huge head start, rather than waiting for the first type to start from scratch, with the second not even appearing until sometime later...which is why so many new tanks experience both an ammonia spike and a subsequent nitrite one.
"Quickly", of course, is a relative term. Tanks that I start in this way typically show a brief and moderate ammonia spike, and no nitrite spike whatsoever; they are almost always completely cycled...to the point where no ammonia is detectable...within a week. So, compared to the alternative...I call that quick.
That observation alone tells me they reproduce rapidly, by anyone's standards. Casual research on bacterial generation time indicates that it is somewhere on the order of 1-2 days, so the significant population of bacteria that one of my tanks begins with doubles every 2 days...which seems in keeping with the water test results. It will naturally seem very slow when the raw tank starts with no introduced bacteria; why would anyone do that? Because they want to buy their bacteria in a bottle? I don't know why anyone would buy canned peaches if they happen to have a peach tree with mature fruit in their yard...so why buy bottled bacteria if you have a mature tank already populated with same?
Thanks for the input; always nice to hear opposing viewpoints and to have a chance to consider alternate ideas. When...if...I have a failure with my method, it will be the first in many dozens of tanks cycled over the years. I'll check back then...just to be clear.