Don't feel dense, it's complicated. I only know this stuff because I've wrestled with it for many hours when trying to explain it.
Your diagnostic code is really helpful. It's telling us very clearly that the Context Access ACL entry that applies to the User's group in the current Context has a Policy that doesn't include save_document.
(More correctly, it's telling us that *none* of the applicable Context Access ACL entries for any of the User's User Groups has that permission -- though there might be only one ACL entry and one User Group involved.)
The good news is that the problem doesn't involve Resource Groups at all. The solution will definitely go on the Context Access tab.
The code needs one addition, to tell us what that Context is (though we're pretty sure it's 'web'):
echo 'Context: ' . $modx->context->get('key');