Yes, the reasoning is bogus because Exxon can't take public office. Full stop.
You - and many other people in this discussion - are confusing different legal concepts of "person" as well as "citizen". People like those in the linked story are working to encourage that confusion.
I don't confuse citizenship with legal person at all.
However, I am assuming the company in the article is thinking it stands a chance, as evidenced by it spending dollars to test how far it can go. Otherwise they're pretty stupid, which they may very well be.
You - and many other people in this discussion - are confusing different legal concepts of "person" as well as "citizen". People like those in the linked story are working to encourage that confusion.