Yes it looks like zettahost does not allow outbound network connections by default. I just typed 'Zettahost outbound network connections' in to google and got:

http://zettahost.runhosting.com/faq.html

15. I cannot connect to remote scripts, RSS feeds or use cURL on my website?

The outgoing connections are disabled by default on all accounts for security reasons, however they can be enabled for paid accounts from Hosting Settings section. So all you need to do is go to your panel Hosting Settings section look for "Firewall Options" and click on the "Enable" button.