The theorem (as ISTM is understood nowadays) is a statement about flat space, so I’d put it as “it doesn’t apply to curved space”; saying that it’s false in curved space sounds to me like saying that “in the US, people drive on the right side of the road” is false in the UK.
There is nothing clear about either of those. Both can be proven without empirical investigation. P’s T is not true in curved space.
The theorem (as ISTM is understood nowadays) is a statement about flat space, so I’d put it as “it doesn’t apply to curved space”; saying that it’s false in curved space sounds to me like saying that “in the US, people drive on the right side of the road” is false in the UK.