You're entirely correct. A very ironic mistake/misunderstanding for the parent post to make.
Edit: I've thought about this a bit more, and you can save the parent post by prepending a result like "Every number larger than one is either prime, or divisible by a prime smaller than itself". In this case you can then assert that your constructed number is prime. However, this result requires its own proof and was not mentioned by the parent post.
Edit: I've thought about this a bit more, and you can save the parent post by prepending a result like "Every number larger than one is either prime, or divisible by a prime smaller than itself". In this case you can then assert that your constructed number is prime. However, this result requires its own proof and was not mentioned by the parent post.