The dangers of overtesting, according to this case by Dr. Malpani:

I sat down with her and explained her results to her. Her HCG and estriol levels were in the normal range and the AFP was marginally lower than normal . The computer calculation showed her levels were well in the normal range, and her re-calculated risk of having Down’s syndrome was actually re-computed to be even lower than expected – only 1 in 2000. This should have been very reassuring, and should have set her mind at peace. However, her doctor did not take the trouble to explain the test results to her – and seemed to use the triple test as an excuse to do even more (expensive and remunerative!) testing.

Maybe that first doctor was trained in the United States – the world leader in defensive medicine.