This is turning into a fun 3-laws loophole discussion.
But I'd like to point out that Ash was a company synthetic (whose nature was hidden from Dallas), and Bishop was a military synthetic. If WY could've gotten to Bishop, I'm sure they would have, either as a backup plan in case of Burke's failure or alternate means of acquiring an egg.
Bishop would've been a lot more successful than Burke, and a lot less obvious due to his nature. It was clear whose side Burke was on from the beginning, no surprise there. He only revealed how far he was willing to go by the end.