Yes, prednisone can definitely be the cause of that and can thin the skin. Other NSAID's can thin the blood and also cause easy bruising. I know for me, Ibuprofen does it.
When I was on pred (started at 40mg per day & tapered off over 8 months), I would bruise way easier and I also noticed my skin would burn or something when I used depilatories (and never did that before). I also have one of those small home microdermabrasion things..before taking pred, it smoothed out my facial skin nicely without any problems. While on pred, oh mannnnn, some parts of my skin bled and I had a horrible red rash all over most of my face. It even caused some little scars here & there. I'll never do that again on pred!