If you are "entitled to the rights or privileges of a subject ... of a foreign power", you are ineligible to be elected to, or to serve in, Federal Parliament. You don't have to have the rights and privileges of a subject of a foreign power -- you just have to be entitled to those rights and privileges.
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Guess what? Much closer to home, under recent and little-noticed changes to New Zealand law, Australian citizens now don't need a visa to live, study or work in the Land of the Long White Cloud. That's right: Any Australian citizen is entitled to live, study and work there.
That means we're ALL entitled to the rights and privileges of a subject of New Zealand -- not a citizen, with the attached rights and privileges such as voting -- but to be a subject of that country, living there, subject to New Zealand law, working or studying. And there's no doubt that New Zealand is a "foreign power" -- you only have to watch the All Blacks do the haka to realise that.
What does this mean?
New Zealand law has made every Australian citizen incapable of being elected to, or serving in, the Australian Parliament. It's not just Barnaby Joyce: It's everyone!
Except this isn't recent, or even a matter of law, but a long-standing mutual agreement with the Australian government, under which we essentially agree to be nice to one another (note: Australia stopped being nice some time ago, both to us and everyone else). So, being nice destroys Australia!