If what she actually posted was “I was feeling bad that I haven’t bought a pass and been bringing Ginger there”, that means the same as “I was feeling bad that I haven’t...been bringing Ginger there”. In other words, she has not admitted anything. I hope she sues the crap out of the Will County Forest Preserve District Police.
IF your version of what she posted is true, she could fight the ticket, and she should.
But in the end she should probably just buy the pass and bring the dog to the park. Assuming they’ve got that cough situation cleared up.
I have no idea what kind of a place this is, you have to get a permit to walk your dog in a park?