The reason you are getting an ICMP respose from 1.1.1.1 is that your router is responding. This is consistent with the explanation. If you still want to doubt it, clear all DNS and ARP tables, ping 1.1.1.1, and check the ARP entry for it. It will match the MAC of your routers inward facing interface.
The fact that the reverse DNS is correct doesn't mean that it's reaching the real deal. The fact that the ping time is fast enough that light could only have traveled 5 or 6 miles one way means it's almost certainly not the real deal.
