As a type 1 diabetic for most of my life, I agree with the above statements. Diabetes is an autoimmune disorder. Like Closet said, cut, bruises take forever to heal because the immune response just sucks. It's why colds can last longer, it's why diabetics are more susceptible to other diseases.
All this would not affect getting injured but it's certainly possible it's affecting recovery time. There are tons of increased probabilities but never any definitive times where you can 100% blame it on the Diabetes