It's *one* reason, not a primary one. The Americans are fully aware that a nuclear deterrent that requires GPS is worthless. US doctrine assumes GPS in peacetime, but not in a hot war. To use Trident as an example, an SSBN will occasionally get a GPS fix to verify its own location. But it doesn't have to, and does so rarely. In wartime, it may *attempt* a GPS fix - because who doesn't like to triple-verify things like that - but a launch can take place without it. To-the-metre location is not required for a successful D5 launch. You get a decent rough estimate of launch location and the stellar navigation can handle the rest. I mean - seriously - they were launching nukes from submarines for *decades* before GPS was around. It helps with accuracy, but given that they quote D5's CEP at under 100m, it can be out an order of magnitude and make little difference to the end effect. (Unless it's a first strike at hardened targets - but then GPS would be available)
To sum - GPS is optional and nice to have, but not at all required for the nuclear deterrent. There are plenty of *conventional* weapons that are near-useless without it though.