Easement or not, if land is specified as public use or parks use, a private citizen/property owner is likely not permitted to fit it with objects detrimental to public safety such as leg-hold traps.
The video is misleading in that most of the traps shown are live-catch humane traps, not the leg-hold type of trap that caused the dog to be painfully trapped. (The trap that injured the dog was the only leg-hold I noticed in the video.) Fortunately the dog and its leg appear to be whole and well, despite the inflammatory terms 'crushed' and 'smashed' used in the story.
Live humane traps would be a reasonable and safe way of dealing with unwanted incursions of wildlife in a public space – although not using baby animals as bait! – but leg-hold traps are IMO cruel, and inappropriate for any space frequented by children, pets, or unsuspecting members of the public. Any company that would place them in such a location is of dubious integrity IMO. To bad the news program didn't bother to clarify the differences between the two types of traps they showed, as a means of informing the public of safe and pain-free alternatives to the old 'trapline' style of bone-crushing, tearing leghold traps – and that trapping and removing problem animals from a property does not have to be an inhumane or deadly practice.
I would love to know why the company agreed to carry out such a job once it became apparent they'd be placing any sort of traps in a public park. Did the property owner who hired them bluster his way through some story about having permission from the parks department? Or, in addition to choosing inappropriate traps for the task and setting, and using bait that should have the ASPCA up in arms, are they in the habit of accepting jobs without verifying the authority of the person hiring them? As I said before, I'm not impressed with this company!
MOO