Symptoms
Name server IPs are not reachable from inside VPS
~# ping <NS_IP>
PING <NS_IP> (<NS_IP>) 56(84) bytes of data.
ping: sendmsg: Operation not permitted
Cause
The problem was caused by incorrect privnets configuration on PCS node level.
Resolution
NS servers were in the same global privnet as VPS backnet privnet:
~# prlsrvctl privnet list
Name G Netmasks
LEGACY x 10.0.0.0/8
vlan1 10.78.20.128/28 *
vlan2 10.78.20.144/28 *
VPS in question belongs to vlan2 privnet, it means that in global 10.0.0.0/8 subnet it can access only hosts inside its privnet 10.78.20.144/28. 10.12.5.7 and 10.12.5.8 NS IPs are inside that global privnet, that's why it was inaccessible from VPS.
In this particular case the privnet may be changed to 10.78.0.0/16 so NSs' IPs will be outside that subnet:
~# prlsrvctl privnet list
Name G Netmasks
LEGACY x 10.78.0.0/16
vlan1 10.78.20.128/28 *
vlan2 10.78.20.144/28 *