I don't think that was the case. The server placed the bill on your table so the server gave you the bill. If ANY party - not just yours but ANY party had walked out without paying the server had given the bill to the party.
So go to the end of the shift and the server hadn't given that bill to ANY party. And no receipt was listed for that bill. Who would pay? The server. Not that ANY party who had left.
The server had to protect his/her butt because of not so nice people. Of ANY party. Not just yours.
But that's the only time we've been given the bill within 10 mins of being seated.