How could an attorney parsing the documents not notice the "in connection with operating the Hosting Service" stipulation?
Further, Bitbucket and Github are opposite in terms of the freedom you have to control your FREE repositories. Github forces your free repositories to be open to the public. Bitbucket allows you to keep some free repositories private.
1.2 What's Included in "Hosted Services". "Hosted Services" include any Atlassian online services products that End User orders, which can include "OnDemand" versions of many Atlassian Software products, the Bitbucket hosting service ("Bitbucket"), and other online services provided by Atlassian. "Hosted Services" always means the version of the Hosted Services as described in Atlassian's then-current product descriptions. End User's detailed rights to use Hosted Services are in Section 3 below.
I'm not sure where you got that quote from, but it's used exactly here: http://www.atlassian.com/end-user-agreement/ So yes, it's used across their suite, and doesn't seem overly broad in that case.