I’m puzzled why you equate “default state” with “nothing active”. If the default should be that thing the button says is on, then have the button default to being in the active state.

The language even for discussing this is tiring to read…

The better solution to "is this the default" is to just have some mechanism for indicating whether the value has been changed, and a way to reset it to its default.

This is quite common in UIs. It also has the benefit of working for all controls, not just checkboxes.

> Hmm, I'd like it if that always made sense, but sometimes the default state, with nothing active, is for Foo to be on.

Then foo will be checked on by default. That's not a problem.

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Is perfectly unambiguous.

What I'd like to see with every option like that is something showing whether it is in default state or not so user can easily glance what was changed from default. "reset to defaults" per page of settings is also appreciated.