I'm not seeing the ambiguity in 'offline' - offline means exactly that, the system is not online (either its turned off or disconnected from the network).
And its real goal is not to protect against such errors (that is what the historical part of a backup like the incremental rsync you described is for). What it is for is protection against a hacker getting into your system and remotely erasing your backups along with your main system (q.f. the recent story re that site of flight sim stuff). Simply saying 'but the target box only exposes ssh/rsync' isn't good enough. All you need is one vulnerability and bang.
You could possibly make an argument in favour of a box which exposes no remote services at all and initiates the rsync itself to a partition explicitly mounted noexec, nosuid; but it is important to realise that that is simply managing the risk down (to ruddy near zero) rather than removing it.
Now for a home setup, its probably the most arguable of all the elements of a backup as to whether you need it. As with all these things, your level of paranoia determines this - I use something similar to what is described above. Yes, I am vulnerable to that type of attack potentially, but that a risk I have judged and made a call on. To think that approach is not at risk is dangerous.