SHA-1 and SHA-2 (SHA256, SHA512) are not the same algorithm. The problem with SHA-2 isn't that it's insecure; it's that it's slow for its current predicted level of security, and that it's MD-strengthened and so requires an HMAC construction to use in applications like MACs. The sentence "It's not like the other sha versions are fixing the overall problem" is wrong.

You would indeed be better off using SHA256.

But not much. It's worth pointing out though that dogmatism around not using SHA-1 is misplaced. There are still no practical attacks on HMAC-MD5, for instance, even though MD5 itself is effectively broken and its use in (for instance) X.509 certificates is insecure.