Richie, I think ultimately it's the 'owner' that's responsible for the dog, not the dopey woman who was walking it unfortunately. In this case it seems that the dog is owned by the St Bernards Trust.
I'd feel the same way as you about taking money off a charity It's a hard one to call

Is your dog insured? If so, make a claim and ask the Trust just to pay the excess fee.
Hope your dog recovers ok.