Integrity and accountability are provided by natural logic, not religious baloney.
I think that you are right...
Religion can make human able to give a particular image of themselves about themselves.... This is one of the necessary workings of a collective culture....
But integrity and accountability, basic moral elementay consciousness, for example are more like mathematical activity: we reap what we sow....
It is impossible for a gardener to fool himself and others and speaking about the garden and not properly working the garden...
A religious man can....
A mathematican cannot....
"Moral imagination" is more akin to mathematical experience or gardening experience than to religious experience...
One of the reason is basic moral activity and moral imagination does not need any kind of collective recognition at all, because his own working is rewarding in itself, like mathematic and gardening....