If difficulty is reduced, I cannot see how it can be anything but an altcoin.
I think difficutly is just one property which a hardfork CAN change. In your definition its also not really possible to change the PoW mechanism with a hardfork. I would be interested to know what people like Gavin or Mike think about this. Maybe they would be on board.
Of course a hard fork CAN change anything. That is part of the reason "forking" with almost no hash power is valueless. (everything would be changed by everyone who knows better!)
Hash power is trust. That is why we have hash power.
So a hard fork, unsupported by majority hash power, is not forking Bitcoin.
Or else we WOULD already have forks of "real" bitcoin classic, unlimited, XT and segwit, for example, and many, many more. All "real" Bitcoin.
Unfortunately, Core have "inherited" the position of control over Bitcoin. (and now respectfully f**k satoshi?)
These incumbents must be ousted to fork Bitcoin, or will be ousted
if when bitcoin forks.