Were fast liners effectively submarine-proof?

How true is the claim that the fastest liners were submarine-proof?

They were not invulnerable, but their speed and zigzagging made them extremely difficult for submarines to attack successfully.

"Submarine-proof" is an exaggeration rather than a technical category. The fastest liners could move at exceptional speed and alter course through zigzagging. Those qualities sharply reduced the time and geometry available for a submarine to obtain a firing solution. Their successful passages therefore reflected difficult targeting conditions, not immunity from torpedoes.