Can nerve conduction tests be wrong?

No: Though there are limitations on what a nerve conductions test can show. If it shows something (and is done by a knowledgeable physician), it is definitely there. It may not be sensitive enough to pick up subtle changes. Not every nerve condition is detectable by this test. If done too soon after an injury (less than 3 weeks), may not show up. If symptoms are worsening, it is worth retesting.