You need to be very clear on what your FBO covers and what they don't. In general, I consider renters insurance worth it given the low cost. Some policies will have a "gap coverage" of $5k to $10k regardless of who is at fault. So, for example, if you are involved in an incident, it's not your fault since you're not PIC, but the school comes after you, the insurance will cover up to $10k. Most schools are insured but have very large deductables; this makes for happy endings for everyone.
Doug
190 hours in the CT and have loved every one.