Absolutely wrong. What gym you pick is crucial. If you are a recreational martial artist, you don't want to be in a gym full of ego driven killers. And vice versa, you don't want to sign a long-term commitment with a gym that's just there to take your money, with coaches and trainers, who don't know what they are doing. Picking the right gym for you is crucial. Visit observe and workout at several gyms, before signing a long-term commitment.
I did it with my son, who was 18 yoa, and a Black Belt in Tang Soo Doo. We did it in Pattaya. Pluses: Very active international gym and fight scene, with many gyms and trainers to choose from. Many inexpensive, but nice accommodations. Good medical options available if necessary. Many good and inexpensive restaurants. Minuses: a lot of distractions. My suggestion, come into it in shape and well trained, ready to go. Personally, visit, observe and work out (if available) at several gyms, before signing a long-term commitment. No longer than month to month.
The mistake you made is offering to pay anything. That's construed as an admission of fault by the dog's owner. Now he is pushing it for more. If facts are as you stated, you are not at fault, thus pay nothing. Offer to pay nothing. "No good deed goes unpunished."