First off, there is no DNS conflict because when you tell your BR player to use a fixed DNS, it also means the BR player is not bothering to ask ANYBODY to fill its DNS entry.
If u use fixed (static) IP however, there is a chance there will be a conflict because the DHCP server may start assigning the same IP you used as static for something else, but of course you can always configure your DHCP with a range of pre-assigned static IP and NEVER assign them as dynamic. But this is needlessly complicated.
Am guessing 99% your router is not configured properly. For example, my router obtains a WAN IP from the ISP, and WAN IP is the remote router your router talks to. There is a field on my router that says use THIS WAN IP as DNS and pass it along to my LAN (LAN=internal network). So the router DHCP picks this up, and when your inside devices ask for a DNS, the DHCP dutyfully passes this info along the dynamic IPs. THAT'S A VERY STANDARD WAY to configure things, but there are many, many ways to muck it up.
Sometimes the DHCP will simply passes on its own IP as DNS, and when a device request DNS service from it, it simply pass along this request to the real DNS it learned from the ISP.
I have a mixture of hard wired and WIFI, everything works peachy.