I don't think it realistically did - it included a system of authorisation that implied a demand that was intentionally denied, however there are multiple other old postal systems which definitely did (e.g. the Imperial Mail of the Holy Roman Empire [1] being one of the significant ones, but that itself built on older systems). A more defensible claim would be the strictly limited claim that the idea of attempting to create a global postal system with global addressability is a new idea. But even long before the UPU, a lot of countries had treaties to allow for forwarding of post, so I think it's unlikely that this idea was new as well, just previously impractical.

[1] https://en.wikipedia.org/wiki/Kaiserliche_Reichspost