This simply is not true.
The hard protocol rules _define_ who is and who isn't a miner. If you violate the rules the system's participants are enforcing, you're not a miner anymore as far as the protocol is concerned.
A minority-miner pow-chain quickly loses credibility. If say a 67% coalition of miners say that a hard-fork will not happen, then the 33% coalition of miners are in a bind, even if the exchanges choose to support the 33% -- which they won't, because it's too vulnerable to double-spend attacks.
Ergo, the minority-miner pow-chain must either also hard-fork the mining algorithm (to require investment in new hardware), or hard-fork to a non-PoW system.
I do understand your definition of a hard-fork. What I'm talking about is a protocol-extrinsic, cryptoeconomic justification of my argument. There's a game of chicken involved, for example.