If that was the case, why didn't they time travel to 1930's New Jersey at the end and just walk on over to Manhattan and get Rory? The reason they didn't is because the Doctor AND River said it would create a paradox which would "destroy New York".
Because he is already dead of old age in that timeline. They cant change that now. The Gravestone places him dead THERE at 86 years of age. The Doctor cant alter it, it would create another paradox. How would they know to go get him without the gravestone, but there would be no grave if they went and got him.
On top of the paradox already in play with them jumping, the new one would blow a hole in space time. Maybe the size of Belgium.