Yes you can insure your kids lifes, your parents lifes etc, you do not have to own it.
All insurances are up to the individual EXCEPT car insurance in UK.
If you don't insure your pump, can you afford to replace it? Same as house contents etc.. If your house burns down, can you afford to replace everything in it.
For those without house insurance there is a separate insurance company that insure pumps. Google it, as I can't remember the name of the company.
I had to prove I had insurance set up for mine when I got mine 4 years ago but not all hospitals do that. Mine isn't classified as a loan pump.
Speak to your hospital.
Loving life