You're completely right, but I'm not really suggesting it; they are being "double counted".

That being said, an individual's share of the "public interest" is incredibly miniscule, and there's relatively few owners, so it's not like it's equal on both sides. In fact, that's ultimately the problem; that we constantly bend due to "corporate interests" that are subject to the whims of an incredibly small fraction of society that is, in general, massively disconnected from the norms of society.

Add on to that, generally having a large amount of money and privilege means that most of the things that are in the "public interest" aren't really of significant concern to you because you can simply buy your way into a completely different system (see public vs private education)

Where double counting is most noticeable is economic arguments. Framing the debate around what maximizes GDP lets the RIAA for example make arguments like “good for the economy and good for musicians.”