If the dealer failed to obtain proof of coverage at the time of sale, Kubota credit might have followed up with a default notice and charged for forced-placed coverage. Will need to look through the entire paper trail on this machine.
Please be careful not to underestimate the severity of skin burns. I had a family member suffer a severe burn. Thought they'd be asking to go to the hospital, but they weren't even though it looked like the pain had to be terrible. Turns out the burn was severe enough that the nerves were also damaged so they weren't signalling pain. Ended up taking them to the ER. The burned area wouldn't heal on its own, either. Required plastic surgery and a skin graft.
If the dealer starts asking you about the severity of your burns, be careful what you say, especially if you haven't obtained proper medical attention.
You have a potential warranty issue, insurance coverage issue, and personal injury issue for which you may want to seek proper legal advice.