For example, my first iPhone, I didn't have a password (I think -- maybe that was my first ipad). It was insecure, but I'm reasonably sure that everything on there was private (in that more physical sense; I have no idea about internal security of those first generations of iphone/ipad).
A weaker claim that is probably true might be: you cannot guarantee your privacy without security. That you cannot have privacy seems like too strong of a claim?
I do agree with you though. Privacy is having your information to yourself. You don't need security for that, just that everyone else keep their nose to them self. But if you want to guarantee your privacy, you need some form of security.
If I send and receive e-mails with a reporter off the record, we are communicating privately. But the communication may not be strictly confidential, nor secure, unless I take additional steps to ensure it.
If I keep files in my home directory, on my own hard disk, with permissions so only my user can access the files, then my files are private. They are not, however, implicitly secure. Another example: an SSH private key. Without a password on the key, the key is private, but not secure.
(Of course it’s impossible to tell that a system hasn’t been manipulated if it’s insecure and that makes the argument bollocks.)
Uh that's not factually incorrect. You can definitely have security without privacy, but not the other way around. Without security that means your privacy can't be protected.