Have fun recovering an encrypted external once you get the click of death. A NAS with at least RAID 1 is a much better solution for onsite.
Online backup solutions aren't shared hosting which is what I assume you're referring to with the "same node as idiot" line of argument. Backup companies don't allow external execution of commands as a hosting company has to, the access levels are completely different. You should have both onsite and offsite for obvious reasons (fire, tornado, tsunami...) and as long as you do due diligence with your vendor, as you should for anything, you'll be fine.
Note that most security breaches that concern customers have to do with database hacks, which isn't possible with a good backup host (two-key passwords encrypted by additional keys, etc. not just a sql database of all customer passwords) or the above scenario (breaching older software on a shared host to gain root and access to all user accounts on that host).
In any case we're getting a bit too specific, a good backup scenario includes onsite and offsite solutions with multiple redundancies.