No, the article is correct. Wikipedia says, “A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) into p in polynomial time.” They cite the paper “The complexity of theorem-proving procedures”, Stephen A. Cook (1971), which says:
It is shown that any recognition
problem solved by a polynomial time-
bounded nondeterministic Turing
machine can be "reduced" to the pro-
blem of determining whether a given
propositional formula is a tautology.
