Gerard,
While you are correct from the standpoint of the general scientific community at the time Einstein was trying to prove his theories, Einstein departed sharply from the strict coordinate view by adding the extra necessary element of the observer (the heart and soul of relativity). Through this addition he saw the Riemann, Kaluza-Klein model of the spatial universe as much more consistent with what he was seeing in the outworking of his theories.
Add to this the fact that by limiting the coordinates to 3s + 1t, it is impossible to rewind the expansion of matter in the universe to a singular moment. In other words, matter doesn't go back to a starting point in that model of the universe.
The extradimensional models are pretty much known to be true and, in some cases, they reveal themselves to likely be more than simply points to plot for marking an event.
Respectfully,
AuldSoul