In particular, open source software tools provide platforms for experimentation that would not otherwise be available. For example, the Linux and BSD kernels made it possible for operating system researchers to try out lots of different ideas on everything from security to memory management with real hardware and real workloads. Without this open source software, your options are 1) write everything yourself, 2) license a kernel from someone, or 3) go work for a company that writes a kernel (e.g. Microsoft, Wind River, Green Hills).
For another example, the Valgrind memory checking tool includes a platform for binary analysis and translation. That platform has let people innovate by building tools that run on large, real Linux programs. I know of at least two academic theses that build on Valgrind (including mine), and there's now three community-contributed data race detection tools.
Both of these areas also have closed source software with innovations, of course. Still, they seem like cases where the open source software platform has lowered the barrier to entry and made it possible for a wider range of people to contribute, therefore spurring innovation.
So I don't buy the broad claim that "open source" software fails to innovate. Maybe we could talk about more specific segments, like office software or microblogging to focus the discussion?