DNS dynamic updates and DHCP

Dracula28

When a DHCP server registers a client's PTR record dynamically (which is the only record it registers for the client, as the client registers the A record itself), it becomes the owner of that record, and will therefore be the only one who is allowed to update that record. Lets say the original DHCP server fails, and is replaced with a new one.

Now when that PTR record is to be updated by the new DHCP server, it will not be able to do so, because it is not the owner of the record. There are two solutions around this

1
make the original DHCP server a member of the DNS Update Proxy Group, because all records updated by members of this group have no owner. When the original server fails, make the new server a member of this group as well, that way the new server will update the original record but not take ownership of the record.

2
Create a user, make it a member of the DNS update proxy group, and then on the Advanced tab of server properties, enter that user's credentials. Now that user will be the owner of the PTR record. When the original server fails, do the same on the new server's Advanced tab.

Have I gotten all this correctly, or am I wrong?