Given other examples, why would you not throw in an "însuşi" for good measure?
You could, but it would be redundant here since both se and sine already hint to himself. In other scenarios it may not be obvious, so însuși could help clear confusion.
If there is one thing Romanian seems to love, it is redundancy. Se and pe sine are redundant to begin with.
As a native speaker, I understand where Răzvan's rationale goes, but for this one I tend to agree with Kevin. Or, at least, the solution could be accepted as valid.