It is true that the GPS signal is below the noise floor, but it has special characteristics which enable it to be recovered as well as or better than a signal without those characteristics which is above the noise floor. In principle, a signal can be arbitrarily below the noise floor and still be recovered, if there is sufficient predictable redundancy in it.
I do think that intentional (non-military) jamming is GPS's biggest potential enemy, but again there are ways to provide resistance to that. A rooftop aerial is the starting point.
As MJ suggests, these things are worth discussing.