As the other dogs were off lead and your dads dogs on lead, i'd expected it could be said the off lead dog was not under control but i'm not sure how it goes if your dog injured the off lead dog as it could be a bit of his word against the other owner unless there's witnesses.

It would probably make your dad's life less stressful having to worry about other dogs coming over if they are muzzled and it can make other owners more respectful oddly as they see the muzzle & think dangerous dog and avoid you. However be aware that your dog is defenseless when wearing a muzzle.