Because by law you are requires to have insurance to drive, ppl like you (and me 10 years ago) who have been REJECTED by your own ins com have to get it from Facility. It is likely you will find no company that will offer you a policy because of the cancellation, i found that out the hard way. They ( ins companies) get together and create this money-eater called Facility and it is the ONLY one that will give you a policy. At a high rate, that's bad news. The good news is if you maintain good driving record, you will be able to go to a "regular" ins comp after 1 year with Facility.
No-fault is very confusing when it's time for me to claim on my policy, either the claim is Direct compentation (not my fault) or not. It is always considered a claim. For a certain period of time and the nature of the claims/violations, the number of claims/violations, demerit points... they might classify you as high-risk and withdraw from issuing your policy, then you'll end up this way. Best thing is to talk with your ins rep or booker (depending on what comp you are dealing with) to get all the fact up front, worse case scenario...etc.
I found out that i should NEVER make a claim on some minor damage even when i am not at fault, better off paying it myself. That is especially true when one already have a history (of CLAIMS for 2 or 3 years, i'm not sure how long). Always remember: a claim for broken windshield is a claim no matter how high is your deductable.
I wish you luck.