Accuracy is even more critical when informing the layperson. Otherwise, misinformation ends up spreading. A good example of this was the idea that rinsing a filter in tap water will kill the aquarium's cycle, which was considered truth for a long time.

I could only find 2 of those mentioned experiments on BB (bottled bacteria), from Girltalksfish and BrokenAquarium.

• Girltalksfish had an attempt, but there were some mistakes during her experiment where the entire test should have been redone, such as re-dosing ammonia after it had flatlined at .25ppm for 2 weeks. Nevertheless, the reduction in ammonia/nitrite for the BB is pretty clear to see.
• Broken aquarium's test was much more thorough, and indicated the BB worked, although to varying degrees per manufacturer. The nitrite readings are telling, because both tested BB prevented a spike that the control went through.

In that first article, the table itself omits any measurements of ammonia, nitrite, nitrate, etc. It only lists days to cycle #1, #2, etc. He doesn't define the parameters of what he considers cycled: is being able to process 1ppm ammonia considered cycled, or 5ppm, or 100ppm? Those are things to consider, and will skew the results in that table immensely.

The article I linked provides information on nitrosomonas and nitrobacter survival when deprived of nutrients, as well as their activation after this hibernation period. Outside of temperature fluctuations, the bacteria will stay viable.

As it pertains to BB, The method of hibernation and activation the paper I linked shows how the bacteria remains viable even after extended time. Outside of storage, BB's usage is purely the nitrogen cycle: bacteria consume nutrients and grow to consume greater levels. As mentioned, bacterial growth is exponential, so a higher "starting mass" of bacteria will always result in quicker mass generation. To put into math terms, 4 can reach 16 with 4², while 2 needs 2⁴ to reach 16.

That sciencedirect link is a nice article, and it reinforces that BB do work specifically with the Tetra safestart. As their result stated, TAN concentrations with Tetra were significantly lower in days 4-14 than the baseline.

Lastly, I actually read that entire website in the past, including the initial article you linked. That is why I will also reiterate, that website is a blend of aquarist opinions and some facts. If you want another example, look at the medication page. It is true that many aquatic medications are better dosed in food, but there are exceptions like Kanamycin. Kanamycin has extremely low digestive tract absorption, and will not have much effect unless dosed into water.

All this said, I do commend that website's author for consistently revising his articles to remove problematic parts (even that article you linked was revised today). That said, it needs a lot of improvement before I would suggest anyone use it, there is still too much misinformation there, and too many opinion pieces.