While keeping everything public is probably good for bioinformatics projects that focus just on building tools, it would be disastrous for other areas of research where revealing a particular gene under investigation or specific genomic locus may result in loss of credit. This problem must be fixed at the publication, CV, and tenure committee level, not by GitHub.
well, I'm not a bioinformaticist (as a matter of fact my personal intent is to develop pharmaceuticals in the public), but I do see it as a chicken and egg problem, in other words, it's possible for github to become an instrument for that change.