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Exactly. You’re precisely right. Which is why:
What makes software open source isn’t the fact that it’s OSI approved, it’s the fact that the source is open for scrutiny.
What? The two things have nothing to do with each other. A GNU operating system doesn’t need to be open source or have its source code available anywhere. A GNU operating system just means it uses GNU tools.
You could write a new kernel from scratch, never distribute a single character of the source code, make an operating system with your new kernel along with GNU tools, and even sell your operating system, which the GPL allows for. The GNU tools would still be open source, sure, but your operating system would be neither open source, nor have its source code completely available.