No.
> SV companies with a global presence surely don’t pay the same in their Bucharest office as they do in their SV office?
That's because local offices have limited hiring pools, because a person living in Bucharest can't practically work in an SF office, and vice versa.
> So does opening a physical office in a remote location suddenly make the idea of having “local pay” valid again?
For positions which must essentially be filled by on-site workers in that office, yes.
> And if not: should all global companies pay equally around the world to anyone who provides the same value within the company?
Rationally, they should offer as low as they think each employee will accept, but be willing to pay based on realized value (net, of course; people in different areas, even remote, may impose different costs.)
Otherwise they'll either be overpaying for value from high-cost regions, leaving money on the table, or missing out on talent thst would produce value in lower-cost regions thst take other offers, both of which reduce profits.