It is true. Think of it this way. The network asks humans to provide security to the network in terms of energy in each step. Since the amount of energy is nontrivial (the whole basis of Nakamoto security), the network promises some compensation to those that protect the network. Nobody is going to mine at a loss (unless they expect greater returns in some reasonable amount of time) so the network security will be roughly the same as the compensation amount because of the incentives/game theory. At the moment, the compensation is a sum of two variables:
1. subsidy - a fixed reward that mints new coins. This variable is design such that it phases out over time
2. fees - a "tax" to incentivize your transaction to take the space on the chain

With time, the subsidy variable disappears into "basically nothing" value and you're only left with the fees. This directly corresponds to the number of transactions as a lower boundary. The network security will be based on it's usage which means on the number of onchain transactions and the competition to capture the block space (bumping the fees as a bribe mechanism).