The fix is simpler than it sounds. Apparently an update changed a file permissions so you need to change a file permissions for one file. Easy to do via FTP.
See http://www.rackmire.co.uk/blog/guides/publicize-error-32300-jetpack-plugin-connecting-social-accounts/#comment-66 for details.
I had found the xlmrpc.php restricted WordPress’ ability to use that file. A simple permissions change was all I needed. Thanks to the website above. No need to test each app or whatever as some sites noted.
Ignore my previous question. I got the PHP updated so no work around needed here. It works now in 5.3.5.
Running into a similar problem. I see that the PHP version is 5.2.17 not 5.2.7 or higher. Is there a way around this zip issue? If not, I will ask the web host providers to upgrade the PHP version.