The values in
.ssh/authorized_keys are public keys -- these are mathematical objects, each of them being linked with another mathematical object called the private key. When the nagios server connects to one of the monitored servers, it uses its private key: the nagios server demonstrates its knowledge of the private key through a mathematical operation (a digital signature), which the target server verifies using the corresponding public key.
The magic of the construction is that the public key can be made public: although the private and public key share a common structure, that structure is "hidden" and cannot be rebuilt from the public key alone (here, "cannot" means "you would need a computer bigger than the whole state of Wyoming, and programmed by Chuck Norris").
So, to log into the target servers, you do not need to grab the public key, but the private key -- and that one never leaves the entrails of the nagios server.
(On the other hand, if you can get a read access to the nagios server, e.g. you can have a look at a backup tape, then you may get the private key, and access all the servers. Attacker's Nirvāṇa. That can be a serious security issue: protect your backups !)