My cat bit the vet tech; why am I liable?

Actually, it was two vet techs. My cat was overdue on his annual vaccines (which I notified the vet upon making the appointment). In addition to his annual he needed a shave, and they knew they were sedating him. We dropped him off in a carrier. I do not have the details of how it happened, but he bit one tech on the hand, sending him to the emergency room. The vet sent in reinforcements, and he bit a second tech, sending him to the emergency room as well. Both bites were minor, no stitches required. Why am I liable for their emergency room bills (and possible lawsuit) when it was an on the job incident, and they *should* be professional animal handlers? I understand and agree with the 10-day rabies quarantine and empathize with their bites, but if they were mechanics working on my car and pinched their finger while changing my tire - would I be responsible?