If the paint scratches on your hood and fenders are covered by your auto insurance it would under your comprehensive coverage. Comprehensive is a physical damage coverage which there is typically a deductible for which you chose the amount of when you started the coverage.

Physical damage coverage is not "fault based coverage." Regardless of fault, if you use physical damage, a deductible is paid. If it is determined that someones elses coverage (property damage liability) should cover the damage then they will try to subrograte the claim. That would mean that it is someone elses fault.

Generally any time you make a claim under your physical damage coverages your deductible will be due. There are some states laws that require the deductible to be waived in certain circumstances, such as in Florida for windshield replacement, or an insurance company may decide to waive a deductible for other reasons, such as if your car was vandalized.

If your insurance company waived your deductible in the past you may request this again but scratches from animals is different than vandalism in that usually vandalism is an intentional act by someone while dogs harming a car would not be.