Are you saying that when Baez referred to "curved spacetime" he was excluding black holes (because the paper was claiming that non--black-holes have Hawking radiation?) or are you saying something else?
well he certainly mentions a result where if there is an everywhere timelike Killing vector field (+ some other assumptions) you can prove that Hawking radiation doesn't occur and that does not include for example the Schwarzschild solution because the Killing vector field partial/partial t becomes non-timelike on the horizon.
So for example if you take a dead star in a vacuum with nothing else in the universe (and make certain technical assumptions) then you can prove that the star does not emit Hawking radiation. That's quite a strong result, and certainly does make the result seem shocking.
(one of my immense frustrations with kubernetes - none of the commands for viewing logs seem to accept logical aggregates like "show me everything from this deployment").