Apex domains cannot have CNAME records.
Question and response
Question
dig ns2.private-nameserver.net. NS
Answer
ns2.private-nameserver.net. 5 NS ns2.private-nameserver.net.
Authority
The response has no authority records.
Additional
ns2.private-nameserver.net. 5 A 199.195.255.66
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0