I think you guys are conflating 'testing authority' with 'testing lab'. Each test is done under the authority of some organization, which could be a national ADA, a national federation, or their international equivalents (WADA, IAAF). But the tests themselves are all performed in WADA-accredited labs. When a country doesn't have a national-level structure to implement tests, the testing authority would default to IAAF, and they would determine which lab to use.
As for covering up positives, I think this is probably easy at all levels. I don't work in a testing lab, but I would be shocked if there were unblinded samples and results floating around ("Usain Bolt's blood", "Report on Farah's adverse findings"). I would expect that on an operational level they're just dealing with coded samples, and very few people are able to break the code and actually link the result back to the athlete. If those few people decide not to act on a result, how would others in the lab know?
Last, if a foreign athlete in the US (for example) tests positive, and the US lab follows all the proper reporting procedures, how much does USADA really know about the result? I would think this is not the jurisdiction of USADA, and rather the confidential finding gets kicked up to IAAF where, in theory, they are supposed to report down to the athlete's federation. But they can just as easily place it in the circular filing cabinet.