After reading about Stack Exchange 2.0 one can conclude that BioStar is part of Stack Exchange 1.0 thus "being owned by individuals or businesses".
There is a recent (1 month) question asking Who owns BioStar? and an answer from Dr. István Albert. I understand that under Stack Exchange 2.0 the hosting company could start running Ads. I am greatly against Ads. Advertisement degrades culture and environment all over the world but the lack of freedom is much worse. BioStar unlike Wikipedia does not have a clear license model. The content of Wikipedia is clearly licensed - the content is publicly owned (Creative Commons Attribution-ShareAlike License) unless it's a logo of NASA or something of that sort.
If BioStar website ceases to exist, it's users and it's content may be lost. At this moment there is no clear right to clone the content. Also the right to Re-mix the content must be there.
The Stack Exchange 2.0 websites get their content licensed under Creative Commons Attribution-ShareAlike License with Sharing and Re-mixing allowed (for an example please see http://photo.stackexchange.com).
Stack Exchange 2.0 could be a great solution because the content gets covered by a freedom granting license (same license as Wikipedia) - inevitably putting more pressure on the Stack Exchange people to provide high quality service and stability.
Will BioStar migrate to a system where the content is community owned?
Edit: Great news!!! BioStar content is now licensed under Creative Commons Attribution-ShareAlike 3.0 Unported License. It's a freedom granting license.