It is definitely true.
A good example, since we are talking about Apple is "the fappening". A massive leak of celebrity photos, including nudes, coming from compromised personal iCloud accounts. It is an obvious attack on privacy, made possible by poor security.
Now, you can tell me that the best way to respect privacy is not to store user data, and it certainly helps, but if your software is insecure, it may be used to harvest passwords or do all sorts of nasty stuff. In other words, maybe you don't store anything but hackers will.
You can't guarantee privacy without security. And even for companies with poor privacy practices, with security, only authorized people can spy on you, without it, anyone can do it.