I'm not entirely sure that the third item is correct. Doesn't that risks you having to repeat that whenever there's an accident?

Of course a dog walking company shouldn't have that many incidents, but if a number of them hit you together you may have a financial problem.

Also, I think that companies are very wary of claiming responsibility because of legal battles. Once they behave like it's their fault, customers can sue them for a large sum.

I'm just challenging a bit whether this is the best way to go about this, although in my own opinion, all three points are correct: You messed up. It happens. But now it's up to you to try to make it better.