The NRA did exercise good judgement.
I don't think it's incumbent on a charitable giver to delve into every aspect of a beneficiary organization. There would be no end to it...
And just my personal opinion, but, if the NRA had said "we'll donate some rifles for the hunt, but we want to audit all your processes, look at your by-laws, see what checks and balances you have, and we want to have our auditor go over your books." I'd say, "thanks but you can keep your rifles."
Before this incident there was nothing to indicate that the Hunt for Heroes project had any issues. I'm sure they will amend their selection process, who knows - maybe people are going to have to show a DD214 from now on... but just looking at the organization, they seem like some people who are trying to do something worthwhile. I can't see where the NRA should have second-guessed them.