If the tank is well established (say 6 months or more) I'm not sure I would necessarily agree with this statement, if a new filtration system could be immediately provided. I think that there would be enough existing bacteria on every surface area of the tank to stave off a cycle, unless perhaps the tank had no substrate.
That makes a ton of sense, if and only if, there is sufficient bacteria in what remains. If the tanks supports 16 million li'l critters

, will they likely be 15 million in the canister, and 1 on the substrate etc.? If so, it will take them 4 x doubling time to regain former strength with a new filter. (naturally, other distributions yield other results. Lacking hard core scientific observation, I was trying to come up with an understanding from empirical observations, rather than conjecture. 'Cause it has been said 'Life will find a way'
The growth of beneficial bacteria is obviously self-limiting once equilibrium is met... However, I also believe that bacterial growth would accelerate once that equilibrium was broken.
Why would you believe that? They can't behave differently than their nature, can they?
I can see two ways that they can behave as if they are growing gangbusters -
1. If the excess bacteria go into hiberrnation when they don't get enough food. Then, they could spring into action when competition decreases, without having to go through a full reproduction cycle.
2. If the extant bacteria hang out, loafing at less than full capacity. Then they could shift into high gear when more resources were suddenly available - and continue with the usual reproduction too...
In any case, empirical observation would confirm that 'rapid recovery'. I am guessing that there is something going on since people seem to have equipment/sickness issues, and recovery is less onerous than the initial cycle set-up.
Again, my goal is just to set my tanks up with a robust framework without putting all my 'fishies in one filter' - and I am just collecting information form other people's experiences.