What happens when you have a "100% test coverage" requirement is that people don't think about the tests, they simply make tests to force the code down every path without thinking whether it was intended to operate like that.

For example if the is-positive-integer had a silly test for "if(value==23) return false", a requirement for "100% test coverage" would simply result in someone creating a test for that condition instead of considering if it was actually a fault.

100% test coverage != no faults.

What you have done by generating 100% test coverage is effectively 'frozen' your code and made it harder to implement any changes.