This is a question structured as a false dichotomy. Software is Open Source if it has an Open Source license. See opensource.org/osd for the standard definition.
The point of software freedom comes into play when software is delivered from producer to user - i.e. it is the license that confers freedom to the user.
The location of the source repository is not significant to being Open Source. However there is a connection.
Both the Free Software and Open Source definitions predate and are not about the more recent rise of social/community programming. Having said that, in retrospect we can see that the combination of them and the Internet may have made social/community programming inevitable.
By now, these behaviours - of cooperation on code by disparate people - are so widespread that some people misunderstand the behaviour pattern as being the "open source" aspect.
So perhaps what you mean to ask is: whether contributing to a private repository is good community behaviour. This is in many ways an even more interesting question.
p.s. it's worth noting the corollary. A public repository of code with no license statement is proprietary code by default - because that's how copyright law works. So to repeat, it isn't the nature of the repository that makes it Open Source, it's the license.
This is a question structured as a false dichotomy. Software is Open Source if it has an Open Source license. See opensource.org/osd for the standard definition.
The point of software freedom comes into play when software is delivered from producer to user - i.e. it is the license that confers freedom to the user.
The location of the source repository is not significant to being Open Source. However there is a connection.
Both the Free Software and Open Source definitions predate and are not about the more recent rise of social/community programming. Having said that, in retrospect we can see that the combination of them and the Internet may have made social/community programming inevitable.
By now, these behaviours - of cooperation on code by disparate people - are so widespread that some people misunderstand the behaviour pattern as being the "open source" aspect.
So perhaps what you mean to ask is: whether contributing to a private repository is good community behaviour. This is in many ways an even more interesting question.
p.s. it's worth noting the corollary. A public repository of code with no license statement is proprietary code by default - because that's how copyright law works. So to repeat, it isn't the nature of the repository that makes it Open Source, it's the license.
This is a great answer!