USAFA has its own fleet of aircraft... i.e. owned by the government. If anything happens, the JAGs (or SJAs if that is the correct term in AF-ese) will take care of it.
This goes for your entire military career. If something happens to you while you are executing your official duties (flying at USAFA is considered professional education... which is part of your duties as a cadet) and you are acting in good faith (i.e. not showing off or doing something illegal), then you will be covered.
You need insurance for outside rentals since regardless of your status as an active duty servicemember, you are renting a civilian aircraft from a civilian operator using a civilian certificate.
The military (as you probably know) has its own method of training and designating pilots as well as its own operating and maintenance regulations/procedures. Military aircraft still follow FARs as practicable, but we can't always due to training and operational requirements.