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Sure you could conduct metrics gathering and analysis in secret. What good would that do? You could be sure that you have some objective handle on how a software project is progressing. However you want the metrics to work for you.
The trick is to be able to share the information on metrics without causing developers to game the system. For example, if you are tracking the number of days to complete a trouble ticket, developers could try to minimize this to the detriment of the project. Developers might only work on the easy problems. Or they could rush to close out other problems without truly resolving the problem. You definitely don't want to do this. But you do want the knowledge of metrics collection to spur developers on to good deeds. This is a tough balance to strike. Perhaps I shall post some more thought on this later.