The people who come up with the spec don't fully know what is required. It's even worse than that actually; the requirements change constantly to account for changes in the technological and business environment within which the project exists.
I think this is a bit of an overstatement, because it implies an often unrealistic separation between writing specs and writing implementations. There may be several levels of each, and the middle levels may overlap.
For example, it may well be the case that the management on a project don't get heavily involved with the technical details and just specify "A needs to communicate with B" as part of the high level requirements. That doesn't mean the technical people responsible for implementing those requirement won't specify detailed protocols at a lower level and wouldn't benefit from formal methods to help ensure correct implementation.