IMO, wood used as fuel also doesn't qualify as low carbon as it also leads to CO2 emissions. So low carbon should not be taken as a synonym for non-fossil fuels.
On the other hand, I'm not so sure that CO emissions are a main concern when we're talking about global warming (it would solve the problem of human effects on our climate a lot faster, though!).
I think low carbon / kohlenstoffarm are just usefull terms that describe things which may not be easy to define exactly in detail, but do convey an unambiguous concept.