Is software developed by publicly funded research groups legally public domain?
No, in general they are not.

It is true that works prepared by US federal government employees as part of their official duties are in the public domain.  This applies, for instance, to journal articles by scientists at DOE or DOD laboratories.  It does not apply to public university employees (they work for state/local governments) and, as far as I know, it does not apply to computer code.