I don't see anything in that says that a UK sub needs US input to launch - in the worst case they don't need any input to launch (they don't have PALs).
Of course, there are dependencies on US systems for lots of things and if the US withdrew support for our Tridents systems we probably couldn't operate them for very long (months - probably, years probably not).
Is it completely "independent" - of course not - it's a US system and there are very few scenarios where the US and UK wouldn't co-ordinate an attack. But does the UK need "permission" to launch - not as far as I know.
The US can withhold targeting data prior to launch, or switch off guidance after launch.
That is all stated as fact in the Parliamentary report. Not sure which part you disagree with.
Sure, you might be able to sneak a launch and hope they don't detect it, but that's a little farcical for a £100bn defence programme I would've thought.
That's appears to be evidence given to a select committee - so it's one person's view.
AFAIK subs don't use GPS underwater - and missile subs spend most of their missions underwater. The missiles themselves use inertial (hence the dependency of knowing the launch point) and star-sighting:
"GPS has been used on some test flights but is assumed not to be available for a real mission."
I'd be very surprised if the sub don't go to see with at least some target data - kinds of defeats the purpose of the entire system which is set up to give UK Trident sub commanders a surprising amount of leeway:
http://www.publications.parliament.uk/pa/cm200506/cmselect/c...