Well here's the deal....
That MAY be a correct statement, but not a rule to live by.
Many people when they add LR find that they get no signficant ammonia, even when they "push" the tank. But this is due to the LR purchased (eg cured with little die off in the new tank) or lack of any major ammonia source to jump start the cycle.
But a lot of LR is not cured, thus, putting it into the tank will result in ammonia production from die off and curing of the rock.
Both happen, but adding LR is not a guarantee that the tank doesn't need to cycle.
Basically the trick is to add an ammonia souce, a big one, IMO...a worst case scenario. Historically this was done by putting enough damsels in that it basically equaled the max stocking level of the tank from day one (1 damsel per 5 gal water). The fish were fed heavily, and this produced a lot of ammonia that then helped cycle the tank.
These days, it is cheaper and more humane (as well as less of a pain to get the fish out) to use dead shrimp from the store, or fish food. Lots of it. Push the tank - challenge it hard - to see if there is an ammonia response.
If no, then the tank, IMO, is "cycled" and ready for fish (which should never be added, IMO, more than one or two at a time).
If yes, well then the tank will cycle, and you didn't lose any fish from adding them and then realizing the tank didn't cycle yet.
But just because you added LR, IMO, does not mean that the tank will not or does not need to cycle. You can do that if you wish, but I prefer to know before investing in livestock if the tank is biologically stable.