He first says that Church was Turing's advisor without citing that Church became Turing's advisor only after both of them independently solved the Entscheidungsproblem.
Also, it is only after Turing became aware of Church's solution that he wrote an appendix to his work where he cited Church and showed that both solutions were equivalent. And even through the solutions were equivalent, the techniques employed were very different. Church even stated that Turing machines were more intuitive and praised Turing's work.
About Turing citing Gödel, the problems they solved were related but not the same. To put it informally, Gödel showed that in every useful axiomatic system, there would theorems that could neither be proved true or false. To do this, he codified math and derived such theorem. On the other hand, Turing showed that there was no general way of deciding if a theorem was true, false on unprovable. To do this, Turing defined a model of computation that we now call Turing machines.
Both Turing and Church defined the first two (and equivalent) models of computation. After this, many new models emerged and none of them were shown to be more powerful (in relation to what it computes) than Turing machines or Lambda Calculus. That is why we now believe in what we call the Church-Turing thesis: Everything that is computable is computable by a Turing machine.
I see many people in the comments praising the article because of the number of citations. This is not a good metric to judge one's work. I do not have the time to make a reference to everything that I said above, but if one is curious they can find all of them in Charles Petzold's book The Annotated Turing. If one is interest in this topic, I also recommend the Stanford Encyclopedia of Philosophy and the book Gödel's Proof.
About the rant the article makes about over attributing a person contributions, I can only say that this is a problem that has no solutions. One example I like to give is Wiles' proof of Fermat's Last Theorem. We say that Wiles proved Fermat's Last Theorem, which is true, but we may also say that Wiles "only" did the last step in proving Fermat's Last Theorem, before him many other people tried, advanced and contributed to our understanding of the problem so Wiles could finally prove it. For me personally, I know that every advance in science is made in the shoulder of giants and do not bother with attribution, since this is a topic we could discuss all day without going anywhere. About the particular example of Turing, I am Computer Scientist working with Theory of Computation and Computational Complexity who is familiar with the history and pioneer work done by Turing and do not believe he is oversold, not in the academic community nor in popular culture.