Can he win? I can't answer that - no one can, but the fact that his dog was in your yard is certainly in your favor. In addition, the fact that he didn't notify you at the time the incident allegedly occurred is also in your favor as is the fact that he has no proof that your dogs had anything to do with his dog being injured. Ignore him unless and until you are actually sued, if you are sued you can submit the claim to your homeowner's insurance carrier BUT be sure to let them know IN WRITING that you do not want the matter settled - I'm sure your neighbor is counting on them settling rather than going to court. If you'd rather not submit the claim to your insurer, then speak with a local attorney regarding your options. The Oklahoma Bar Association can give you a referral: www.okbar.org/
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
Were the police called?
Was Animal Control called?
Has there been any official response to this alleged incident?
Have you been served with a complaint, or even a demand letter?
If the answer to all the above is "No," it may all blow over and notice to your homeowers' carrier premature. If you have received a demand letter or notice of claim, forward it to your carrier. It will provide you with counsel, with whom you can review the matter in detail.
The foregoing is for general information purposes and does not establish an attorney-client relationship.