Well, that's the point they should be making Cynic. Whether or not an island is inhabited has very little to do with whether or not there are dangerous waters and shipping lanes nearby.
http://en.wikipedia.org/wiki/Monomoy_Point_Light
Yeah that just seems like they're rebuilding it for historical value...probably not the best use of emergency economic stimulus funds.
Perhaps by uninhabited, they were referring to the lighthouse (thus making it pointless to do work on its living quarters) - not sure - just throwing ideas out there.
I think you're giving them too much credit.
They just thought that the whole lighthouse project sounded bad enough and used it as a whipping boy, without bothering about the details.