Paint flaking on bumper

A few months ago, our 2011 Sonata had the rear bumper replaced, after an accident. Last week, we noticed an area on the bumper where the paint was bubbling and flaking. We took it back to shop, where the work had been done, as we thought it must have been a problem with either the paint or the procedure that was done.
However, they claim that it was an accident that caused this to happen.
I am attaching four photos. The section where the paint is peeling, it should be obvious...what isn't as clear is the area where they claim that the bumper was hit. It is directly below the peeling section, just below the lower bend in the bumper. On the picture with the flash reflection, the scratch seems more obvious.
My question...could a small scratch, such as the one on this bumper cause such extensive paint peeling above it? Shouldn't the paint adhere better than this (if this scratch could have been the cause??)?
If a scratch like this should NOT cause the paint damage well above the site, what action should I take now? Obviously, if it is a problem in the procedure they used to do the paint job, they should take care of it without cost...I cannot afford a lawyer, and I really do not want to get my insurance company involved...
Can you help me by giving me some advice?
Thank you.

If insurance paid for the original replacement of the bumper, then I would most definately get them involved. Hard to tell from the pictures, but I'm not seeing any other damage that would cause the paint to peel in that large of a section. If you get your insurance company involved, then the body shop will be more likely to repair it on their dime because they will want to keep the insurance company sending them work. If a body shop pisses off an insurance company too many times, you can guarentee that insurance company will be sending their cars elsewhere.