There were two phases though: the initial rollout, and sometime later the coverup.

If they had asked very reasonable questions about the software during the rollout there would have been no need for a coverup. No software rolls out without any bugs and it's really reasonable to ask why so many post offices had missing funds and if they were sure if it was real or not. The PO leadership basically ignored all evidence that there were bugs from the very beginning, and that makes no sense until you realize that they were starting from the premise that the postmasters are thieves and this software is going to catch them.