@duraleigh can you tell me what exactly you find "erroneous" before completely disregarding my answer? I am the only person who actually addressed the OPís problem, rather than ranting about pool shopís and testing methods.
OP can test the pool a thousand times, but it won't make the stain go away... Test results are never 100% perfect no matter who or where you get the test from. There will always be inaccuracies. I don't disagree that in a pool shop where there is a speed v efficiency trade-off, the testing can be wildly variable. I think giving someone advice that they should "run" from a pool shop because of the testing alone is erroneous. Just because one hairdresser gives you a bad haircut, does it mean that every hairdresser in the world can't be trusted? Making a blanket statement about all pool shops with "overwhelming evidence" of bad testing is simply confirmation bias in my opinion.
For precision, it's always better if the same person performs the test. If you truly want a more "scientific" water test, you should take 3 samples and perform 3 tests and then find the average result for each parameter. But in my opinion it is just as important to look at the water test history, not just the individual results when it comes to problem-solving.
To re-word what I said previously, most stain treatments I have used say that you need to have the chlorine <0.5ppm (because they cause cloudiness if added when the chlorine is high). Then, once the stain is removed you can increase the chlorine again. However, if you rapidly increase the pH, (which will happen when using calcium hypochlorite or sodium hypochlorite) the stain can come back.