I am sure there are many definitions for a great tester. All of them are true in a certain context. All of them are also flawed. The idea that a sole individual can be responsible for the quality of a product is flawed.
As soon as there is more than one test person, it is important for the test team to have a shared understanding of what needs to be tested and who will be doing the testing. In some organizations, a written test plan facilitates that understanding. A person who can write test cases and organize them into a test plan provides a valuable service. If a tester does a great job at writing test cases, one might call that person a great tester.
At the same time, written test cases by themselves are just words on paper -- nothing more. A document -- whether a test plan, a design document, or a functional specification -- is rarely a substitute for internalizing the goals, trade-offs, and personalities that guide a product to its current form. For all but the most trivial cases, one cannot internalize a product's goals and trade-offs overnight; the learning process takes time and requires interacting with the others on the team. Moreover, every test plan is incomplete and flawed, biased by the author's perceptions, interests, and experiences. A tester who starts with someone else's flawed, biased test plan, reads between the lines, and despite the tedium and repetitiveness of the job, finds bugs in places that that test plan only hinted at -- or omitted entirely -- is also surely a great tester.
Quality is a team effort. I do not mean that everyone shows up at the office and salutes inspirational quality posters. Rather, unless everyone works together, it is virtually impossible to produce a good product. No one person can take sole credit for a good product, and no one person can take all the blame for a bad product.