a default routing setup will route regardless of network and host address; the rfc indicates that the reserved blocks _should_ not be routed in public networks; and are in most cases implemented as such on the public routers on the Internet.

the traceroute output in the original post indicates that the 10 dot network host is within a local context to the two adjacent hosts listed.

aside from that, in this example we are not routing _to_ the 10.x.x.x network - we are routing through the 10.x.x.x network as a private infrastructure; because this host/network is local (physical) on both ends to public address space, the IP is irrelevant other than being associated with a mac address in the arp tables of the two adjacent hosts listed.