If you're taking Warfarin, you have to get your INR checked every two to three weeks. It's really not practical to do that at three different labs every time. Also, this isn't some exotic edge case that only applies to a few people, but an extremely common medication. We're talking about huge numbers of patients here. If all their tests had to be triple-checked, the costs would be enormous.
See https://news.ycombinator.com/item?id=11243904 above as to why the cost issue is a risk assessment / return analysis. In certain scenarios in which potential harm is high from an incorrect diagnosis, it's worth the cost to perform the test completely independently.
