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People keep saying that, but it is simply not true.
With a given number of "front-end" CPUs checking ECDSA transaction signatures, miners will be able to process at most N transactions per second.
If there are more transactions than that going over the network, then miners will drop the least-profitable transactions and only process the most-profitable N.
Mining involves two distinct tasks: checking transactions and gathering them into a block (which is inexpensive right now because there aren't gazillions of transactions). And then hashing (which will always be expensive).
Miner operators will keep track of the transactions they're dropping, and will do some math to figure out if it would be profitable for them to invest in MORE front-end CPUs to process more than N transactions per second.