I'm pretty sure the ER doesn't care, but your insurance would. Normally those questions show up on forms so your insurance company can decline to pay a claim or go after someone else to pay for it. If it does turn out to be a work comp injury the insurance folks can sort things out later, though it may involve some extra paperwork.
In fact, your insurance company may send you that paperwork to have you verify that you REALLY MEAN IT when you indicated they can't go after anyone else for it. I had something similar happen when I was walking down some stairs at the zoo and just missed a step and turned my ankle. Totally my fault--I was holding onto the damn handrail and everything (had my then-18mo son in my arms), and the zoo wasn't negligent in any way, but boy did my insurance company want it to be the zoo's fault.
If you were off the clock but were at your store for your shift or to talk to HR or something work related, the injury should be classified as WC, but if you were just shopping it wouldn't be, I don't think.