Only oddity was the reference to the "router cache". I agree if your browser tried to lookup example.com the local cache would be used, but then it would be the system's configured DNS server - and that would most likely be an ISP, rather than your local router.
(Assuming a typical home connection, your router is _probably_ not a DNS server with local cache, it probably is a DHCP server which will hand out the upstream/ISPs' nameservers.)