It's the differential pressure that inflates a tyre, not the absolute pressure. Climing to FL200 will add another 0.5Bar to the effective inflation pressure, so at 65psi that's only another 10% or so. Not much really.
Re: Space Shuttle tyres, if they are already at huge pressures, then putting them into a vacuum is only going to add 1Bar to the inflation pressure - didly squat in the scheme of things.
A