Been told the same thing (ANR only gives the impression of increased protection) before I got my ANR headset a while ago. I accepted this until I really thought about it - what allows ANR to reduce noise is an out-of-phase waveform being "added" to the original waveform - so the resultant amplitude of the wave hitting the eardrum is greatly reduced. We know this works, as the headsets are very quiet. So if the amplitude of the wave is greatly reduced, then this provides "actual" protection, as it's loud (i.e. high amplitude) sound that causes hearing damage.
I've also seen ANR described on some US aviation medical sites as an "expensive but effective" form of protection.