Interesting. PlusNet's four DNS servers 220.127.116.11 or 18.104.22.168 or 22.214.171.124 or 126.96.36.199 don't provide an answer, as you noted:
dig @188.8.131.52 git.zaptic.com.
however PlusNet's two Safeguard DNS servers 184.108.40.206 or 220.127.116.11 and the public DNS servers I tried 18.104.22.168 or 22.214.171.124 or 126.96.36.199 or 188.8.131.52 or 184.108.40.206 etc do all provide the answer
dig @220.127.116.11 git.zaptic.com. git.zaptic.com. 299 IN A 172.31.45.2
but, my own router running OpenWrt stops the answer passing through with a log error of "dnsmasq[...]: possible DNS-rebind attack detected: git.zaptic.com" because as you mentioned, it isn't a public IP address, it's in the private address space of RFC1918 & RFC6761: 10.0.0.0 - 10.255.255.255 (10/8 prefix) 172.16.0.0 - 172.31.255.255 (172.16/12 prefix) 192.168.0.0 - 192.168.255.255 (192.168/16 prefix)
So I'm tempted to think that it is correct for an Internet DNS server to not provide an answer, as you couldn't reach there on the Internet anyway.
Interesting that the the public ones and the Safeguard ones do answer.
As for setting your routers DHCP settings to hand out alternate DNS servers, I think that some PlusNet routers can do that (perhaps the 2704n can) but I think I've also read that other ones PlusNet provide can't - you'd have to set the DNS servers on your PC instead for example. (I'm not currently using a router supplied by PlusNet)