I don't think so. There's a reason you're supposed to up defense but not protection when you're training for master of critical hit title.. that way the monsters will still have maximum critical chance, but they will still do 1s on you when they critical. If defense were completely ignored on a critical hit, there's no way that rats/mimics would do a 1 damage critical on you. I'm not sure where you're getting your info from but it doesn't sound like a legitimate source.
It's speculated that defense is ignored on Critical Hits. If it's true, then the critical portion (150%) would ignore defense, but still get reduced by protection.
Mimics not only have very low damage, but we also don't know the rank of their Critical Hit skill. At Rank F, they would only gain 50% bonus damage. Given that mimics only do about 8 damage, a crit would only add like 4 more damage.
Also, I do take 6-12 from Mimic crits, while I usually only take 1-3s from noncrits, with around 4 Defense and 0 Prot.