Hi. Sorry, but I'm not mixing the two. The DHCP server on my local router assigns the IP address, gateway & DNS address as you would expect. Calling Ethernet.dnsServerIP() returns the DNS server IP address as set by the DHCP server (192.168.1.2 in my case).
If the device has Internet connectivity and only needs to resolve names on public DNS (e.g., google.com), then you will not see any issues. However, internal names won't resolve even if they are configured on the DNS server configured in DHCP.
When I sniff the traffic using Wireshark I can see that DNS requests go to those 3 IP addresses, not the DNS server configured on my DHCP server and reported by Ethernet.dnsServerIP().
I have no idea where they are coming from as I haven't configured them either in my code or on any network devices. My assumption is that they are hardcoded somewhere either in the Ethernet library (I couldn't find them) or the mbed OS itself, but that is just a guess.