Dear scope of guarantee liability:
The precise language in the guarantee will control. You should buy insurance because the guarantor is often left holding the bag. The renter must purchase a homeowner or renters insurance. You should be identified as a named "insured."
Most attorneys would caution you to heed the maxim that no good wind blows toward a guarantor.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.