This is much better than a coin flip. A coin flip would give about 50% true positive rate (which is about the same as the test), but it would also give about 50

This is much better than a coin flip. A coin flip would give about 50% true positive rate (which is about the same as the test), but it would also give about 50% false positive rate. To put it in perspective, imagine 10 people have cancer in a population of 1000 (a rate of 10% which is too high compared to what I think the real number should be). The test would fail to identify 5 of the people with cancer, and it would say that 5 of the people without cancer have cancer. So overall it would misidentify 10 people. The coin flip would misidentify 500 people. Amusingly in this example if you have a "test" that just says nobody has cancer it would also misidentify only 10 people :) I think this is why they are reporting true positive rate and false positive rate.