For the few among us who have yet to beat the game, spoiler warning.
To scare little childs The Order called blasphemers. Sure, I'll bet some Order members were scared of him, but he seemed to do the will of The Order rather than punish Alex for something. Maybe if he killed Josh over and over, but what he does is, on the one occasion he actually does something, he kills someone The Order wanted dead.
I'd never guess? What source is this? Ishmeal does make sense, but it seems that there's no common belief about what was said. I find it surprising no-one's mentioned the whispering in the apartment yet. Y'know, Comeseemydeadwifedosomelaundrytoescapesee(Some name's)face...
Pyramid Head a tool of The Order?! Are you kidding me? He's The Order's worst enemy! Did you not see the carcass he left behind in the Prison? And , considering the fact that he's based off the movie version, the way The Order calls him the fiend!