If a security vulnerability happens on the public Fogzbugs instance, we'd be bitten by it badly in this sort of situation. In our setup, we protect against that by exposing the JIRA webserver and git servers only inside of our private network.
It's not about perfect security, but it does greatly reduce the attack surface when the server isn't even accessible via the internet. I can't prevent anyone who wants to from signing up for the free trial of Fogzbugs and exploiting their publicly running system - even logged-in-only exploits are possible in such a case.
Not to mention the issues with downtime on these cloud providers. My provider has had 1 sizeable, noticeable outage in the last 5 years. It spanned about 20 minutes. Look at a big, popular cloud service like GitHub - they've had several in the past year alone, spanning hours at times.
I find these sorts of compromises where I'm offering my code and server configurations to a 3rd party company (where basically any admin there is free to read it, or anyone who can compromise their admins) to be rather poor. I'd rather keep the blame within my own company and be in control of our data fully rather than having to worry about whether Fogzbugs operations follows proper security precautions, I only have to worry about whether we do.
Call it paranoid if you want, but I think it's a more than reasonable precaution to not just throw your data around to anyone who asks for it. Especially data which could lead to compromise of servers and customer information. I value my customer's information much more than I value any gains from some easy to use cloud service.