While I can see where you are coming from and agree with your sentiment, one issue that comes with this approach is complexity. A lot of people are not even in the know about what open source software even means.
Also it leaves a lot of room for potential flamewars about what kind of open source matters for which category, and why.
This is why I would personally lean more towards a singular definition to follow, be it the OSI or something else, and follow that.
While it is problematic that we have not defined this yet, I do not think that its so important that we have to immideatly freeze this requirement everywhere on the site, as it does not have that much of an privacy impact to the currently recommend software. All software thats recommend is open and can be read to a large decree to check for nasty stuff, this is most a discussion about licensing.