Sorry, I didn't want to be too technical. You should consider how DNS works.
If you create a zone (yourdomain.com), this zone will be yours on your DNS server. The NS2 and other backup servers will be get it with zone transfer and they think them as own zone, like yours. This servers are the authoritative servers. If they need this zone, they know this zone is ours, and look them locally. But there is a parent DNS server for the zone. In this example the .com. The .com DNS servers know you are the authoritative DNS owner of the yourdomain.com, and if the yourdomain.com serial number is grown, they get the zone with zone transfer, to have the new version. They cache the zone, for other servers, but with a TTL. After some time, the TTL expires, and they get the zone again from the authoritative DNS server, in this example, yours. If they can't, they think this zone is no longer available, and delete it from their zones.
That's the reason, you can't use this pubic DNS servers as backups. Only authoritative DNS servers can work as a backup. Every DNS record knows who are their authoritative servers, it's in the zone. (The SOA record).
This explanation could be lead far :)