Come to think of it, I've had several emergency visits where I have not had to pay until later:

I've not had to pay at time of service when my emergency visits to the Tierspital happen in the middle of the night, despite it being policy to pay before taking the animal home. There is no admin staff there at 2AM to process a payment, so they simply send me a bill.

Ditto emergencies at Hünenberg, again despite policy. When my sitter had to bring Haifisch in - again after hours - for what ultimately ended up an amputation and long hospital stay they simply told her not to worry, they would settle the bill with me later.

And once I found an injured cat while out walking the mutts. I just scooped the cat up and dashed to the vet, forgetting that I never carry my wallet with me on walks. No worries, the cat was treated immediately and I paid the next day.

However, in all cases I was a regular customer with a good relationship with the practice and a good payment history. They knew there was no risk.

If I had gone to a new vet or clinic where I had no history, though, I doubt I would have received the same consideration.