"If your organisation uses a piece of open source code and that code contains or in any way touches proprietary code that you're using, then, potentially, there's the obligation to make the proprietary code available to the rest of the open source community"
Well, he's right in a way. Potentially, if you distributed that code to some recipient and didn't include the full source code for your proprietary app, the only way to satisfy the GPL is to make a written offer valid for any third party for the complete source code.
licences only apply to recipients not to the whole world.
Yes, but 3b of the GPL applies to the whole world assuming you didn't satisfy 3a or 3c.