This one's a simple one:
"Injury or Sickness of an Insured, Traveling
Companion or Family Member traveling with the
Insured must be so disabling as to
reasonably cause
a Trip to be cancelled or interrupted, or which results
in medically imposed restrictions as
certified by a
Physician at the time of Loss preventing your
continued participation in the Trip."
I remember grade school where I had to get a note from my mom when I was sick to get excused for missing school. Maybe it's the same thing?
As for the cancellation thing, it seems you didn't read the Spirit policies right:
"You can cancel reservations at least 24 hours or more prior to the scheduled departure time
online, at the airport, or over the phone
for a fee. When you cancel your reservation, we will provide a
Future Travel Credit. Use of this credit requires that travel must be booked within 60 days of issuance for travel on any flight available in the system.
Even if the value of the reservation is less than the cancellation fee, we will still provide a $10 per one way (maximum $20) voucher to be applied towards future travel for online cancellations."
You were going to be charged $10 for cancelling over the phone where you could have cancelled online for no charge. You would have also received a 100% credit for the full value of the ticket. This can be done up to 24 hours before the flight.
Most airlines sell tickets that are "non-refundable" that you won't get a refund either way. Spirit is no different, actually they are the same in this respect.
So if you would have gotten a doctor's certification and provided it to the insurance company, they would have refunded you the money, up to $300. If you could have also cancelled the reservation online at least 24 hours before the flight, you would have gotten a full credit to use on a future flight.
What's the real problem here?