Stan,
I still don't understand why a man who wasn't the father would enter sureties. As I said in the thread you quoted, "I've got a Bastardy Bond dated 1806, where my g.g.g.grandmother names one man as the father of her unborn child, but he and another man entered surieties". As the two men appeared to live in different Parishes it seems totally illogical.
It makes no sense for someone who is not the father to offer to indemnify the Parish against its extra costs. It certainly wouldn't happen nowadays. If someone was pregnant who had doubts regarding the actual father, I'm sure the men who might be the father, wouldn't get together and agree to share the costs between them.