If a cow is fed grass at any point in its life it can be called grass fed. Normally cows are finished on grain for the last 90-160 days before slaughter. Finishing them on grain fattens them up significantly and it decreases the Omega 3s and CLA found in the meat. Organic doesn't mean anything other than the grain fed to the cattle is organic.
I don't know that any place just grass finishes their beef though it has been proven that just a few days of switching from a grain fed diet to grass fed diet, right before slaughter, reduces the chance of e coli significantly. It is not cost effective for the big CAFOs (Concentrated Animal Feeding Operation) to finish on grass.
The best thing to do is to get to know your local farmers, ask about their practices and/or buy your meat from a reputable source online.