I mean “valid” in the mathematical/logical sense. It does not follow from the stated assumptions that n > 1, in the inductive step is this proof.

This has nothing to do with the idea that it can be common practice to prove claims of the form for all n > N, P(n) by induction when N is a number like 4. Yes there is a perfectly valid way to use proof by induction to do such proofs. Has nothing to do with this blog post.