LOL, yes, I do see that you are coming to some conclusions but one has to be certain ;-) All experimental designs are subject to several factors. The sampling requirements for a false positive or false negative are different. Large numbers of trials necessary for statistical certainty can get expensive. One seldom gets many samples of an endangered species. This means that one must have enough confidence in the lab to regard their conclusions to be totally reliable. That means that one should qualify the lab in advance of the study.
If this were a lab qual, I would first make a call on the lab to see if they have validated their procedures by indepedent third-party audit. I would cross their process documentation with the handling of a sample that was already in the lab. I would look at calibration data, request their SPC charts, check the training logs on the technicians, and go through their audit file. If they've got all that, it looks clean, it cross-checks when I call the auditor, and I know their reputation or have experience with them, I'm done.
Lacking any of that, I might perform a set of extreme vertex screening experiments to see if I wanted to go into further tests. I would ask them what the minimum mass of the sample must be. Some of the submissons might be marginally below that (to see if they react to their own specs). I might take the two fur samples and break them into four tests: lynx, bobcat, both, and a second bobcat (assuming that lynx samples were harder to get). I would NOT tell them what I was sending. The vials would be merely numbered. (Remember, you are sampling DNA, the lab tech is unlikely to recognize the fur.) This test verifies that the lab is capable of identifying both species and individuals, and that they will react to out-of-range data (the mixed vial) with a response of, "invalid sample, but it could be this." If I get all that, I would repeat the test with but two of the samples from one of the same individuals as before. That way I get data from different sample preparation procedures and perhaps different technicians and I get to see how well the equipment repeats in separate trials.
Screening experiments are an artform because few can afford the number of samples required for statistical certainty. The setup I just described is a pretty rugged indicator of the lab's performance.