I like how you’re getting both sides of this issue and showing how it’s more complicated than it seems at first.
For more, see this thing I posted on my blog last night.
Error: API requests are being delayed for this account. New posts will not be retrieved.
There may be an issue with the Instagram Access Token that you are using. Your server might also be unable to connect to Instagram at this time.
Error: No posts found.
Make sure this account has posts available on instagram.com.
Error: admin-ajax.php test was not successful. Some features may not be available.
Please visit this page to troubleshoot.