The problem is that they are wrong only about people suffering because they have upset some god(s). The rest is a nice and apt cosmological metaphor:

1) humans can blame themselves for suffering because all suffering is self-inflicted, it's a choice

2) when you "serve God," that is to say, honor the causal rules of universe, etc., nothing obscures your view of oneness which also reveals our immortal nature

I'd also say that one does not have to be influenced by "religious teachers" to not see our oneness. All our societies teach separation by default. Therefore there's a lot folks who suffer.

But yes, religious so-called teachers perverted that metaphor beyond recognition. Well, poor folks, their income, social standing, and/or sense of worth depends on it.