A false positive costs much lower than a false negative in this instance so it should follow that FP should be more common. However, without the data it is still speculation.
Whether false positives or false negatives are more harmful is a difficult question. A false positive might stop millions from taking a life-saving drug. A false negative might cause millions to take a life-threatening drug.
By nature a false positive interaction could be re-tested more easily than a false negative though, correct? Also, that fits in with medical "first, do no harm" framework more readily.
Regarding your second point, I agree. But it must be balanced against the other tenets of medical ethics. At any rate, this seems to be an important study. I look forward to seeing the same study carried out across different EMR databases and then meta-analyzed. That will be extremely powerful.