My example of this was far simpler
When testing out a new banking system urgent call comes in.
The name and address for customer &^%&%& is always printing out wrong! - urgent.
The evidence appears to be there in front of me, it is indeed wrong... Everyone else appears to be working perfectly.
A really good rummage around in the underlying database follows.
The name and address were input incorrectly in the first place (slaps forehead).
Took 3 days to convince the customer with evidence that this was not a candidate for the "reasons we will try to cut the bill" list and indeed had the opposite effect of wasting several days at quite a high rate simply to diagnose a data input issue.