But the author claims that something is equivalent to P=NP! Now, P=NP does have a very "literal, narrow interpretation" (read: it has a very precise meaning), in fact, this is the only interpretation in which it makes sense at all.

So if you claim that something is equivalent to it, you better be prepared to define what exactly "something" is, and give a rigorous argument as to why it's equivalent. Some hand-waving with vaguely defined and ambiguous terms just doesn't cut it.