My house backs up to a canyon as well. Are you referring to the shrubs in the canyon as brush? I don’t know what the rules are but it’s not dead although it will turn brown in the summer. Never did anything with the vegetation in the canyon. I thought the HOA is supposed to take care of that since its not my property.
I just got renewed with Chubb a month ago, no problems. The canyon looks the same now as when I signed up with Chubb three years ago so I don’t think any maintenace is needed.