Do PCs and Their Adversaries Need to Operate by the Same Rules?

Think of this as a follow up to yesterday's post on critical hits.

In 4e, monsters follow their own set of rules. Mooks always die with one hit, and bosses have abilities on par with PCs or better (yeah, this is a generalization - but it serves it purpose). Do we need to have the PCs and the monsters playing by the same rules in the OSR?

If you want to use critical hits for the PC attacks, you could limit crits on the opposing side to the Big Bad Evil Guy or the equivalent. Or you could give PCs a crit on a natural 20, andmake their adversaries confirm their nat 20 crits with a second attack role. You could even give PCs a save (vs Death or whatnot) instead of having the monster role to confirm.

The thing is, once you let the PCs and their adversaries play by different rules, you do change the nature of the game.

By the same token, by adding critical hits into a game that wasn't designed for critical hits, you are already changing the nature of the game. Critical hits hurt the PCs more the they hurt their adversaries. Is changing the rules the two sides operate by a way to balance that discrepancy, or does it cause more problems then it helps?

Can you tinker to the point that the game is no longer "The Game" we know?