If you select a specific DNS server pair in AmiTCP then this is what will be used, regardless of what the router wants to use. Your ISP may or may not manipulate outbound DNS queries and the corresponding results. It's technically possible, and if you're living in the UK, it might actually happen.
I have actually come across some routers which defy this rule. Some older Engenius routers (I stopped using the damned things, so I cannot speak about newer units,) some Belkin, and a couple of D-Links were culprits in breaking Windows Server DNS services. I was able to show that the routers were intercepting DNS packets. I some cases the inbound was blocked, forcing the server to use the router for DNS. In other cases, outbound DNS packets were being usurped, and this caused huge issues with EDNS queries as none of these routers support EDNS so queries would be delayed, broken in sequence, or in most testing simply dropped.
It's easier to tell what's happening with your queries if you have access to an outside DNS server's logs. But it's not impossible otherwise.
