Hello David
If the GRE tunnel is established over the Internet, then it is unlikely that an OSPF configuration would cause a recursive routing error since you wouldn’t have OSPF running on the Internet, or on your edge devices. However, the recursive routing error is not limited to OSPF. It could occur with any routing protocol, as well as static routing.
The truth is that it is not a very common error because, in most cases, edge devices will have a default route configured sending all traffic destined for the Internet via the Internet-facing physical interface. That will typically be enough to eliminate such an error, since routing over the GRE tunnel is achieved using a more specific route. However, if, for some reason, you have a more specific route (either learned dynamically or configured statically) to the tunnel endpoint via the tunnel itself, the recursive routing error will occur.
The key here is that recursive routing errors in GRE tunnels stem from a router or routing protocol choosing the tunnel as the path to the tunnel’s own endpoint regardless of what routing protocol is used.
I hope this has been helpful!
Laz