Christopher:
They've even made an extra effort to keep shows that have struggled in the ratings, like Terminator: The Sarah Connor Chronicles, Dollhouse, and Fringe. Which is why it's so unfair that the "FOX kills genre shows" cliche is still so widely accepted even though it's been more than a decade since Firefly and the responsible execs left the company a long time ago.
Well, therein probably lies your confusion. You're citing one show and executives there/no longer there, as our source of complaints. This has been happening before, during and after "Firefly", so it's a continuous string of people, which has earned the reputation FOX has gotten over it. Yes, some things deserved to be cancelled and should never have been greenlite to begin with (I won't name anything since there's always somebody out there who lieks crap), but there have been a number of promising shows or good shows (such as "Firefly").
By the way, one lady who is no longer there (as I recall) said she was the one responsible for cancelling "Firefly". I watched her in a Youtube video go on stage at a convention and tell the fans that; she was not well recieved.
Now, some networks have tried to rectify this by -- on very rare occasions -- bringing back a series from cancellation years after-the-fact, such as: "Family Guy", "Futurama", and "Samurai Jack" (though not all shows are quite the same after they come back). Oh, and "Due South", but I think that switched networks.