There was a guy I heard years ago who, when asked about AZA, dismissively referred to it as "a country club for zoos." We all kind of scoffed at him as a crank. Ten years later, everyone in the US knew his name (or at least his pseudonym), Joe Exotic.
There are some great un-accredited facilities in the US - and a whole lot of mediocre ones, plus a few truly awful ones. Some facilities have great enclosures but poor welfare or shady logistics. Some are upright and honest, but don't have the money or resources they should. I usually tell folks that if it's AZA, I trust them (not that I haven't encountered some skullduggery in AZA facilities). Non-AZAs, I take on a case by case basis to separate the good, the bad, and the ugly.