When I first watched it, I went with the flow, even though I was a bit irritated that they didn't check the baby out properly.
Now, I definitely don't agree with his decision - having read a bit about Chinese history, and the fact that the downfall of many dynasties was caused by a succession of CHILD emperors and their corrupt/useless advisors, I can see the same thing happening here, even without the boy-king being infected with zombie worms.
Basically, Lee Chang should have said that the baby was his, that he spent some time sowing his wild oats, and that the evil queen stole his baby and had his sidepiece killed. There. Problem solved. King Lee Chang would have noticed the problem with the boy, because Seo-bi would have visited frequently in between looking for the whatever.
I can't believe they left that moron (Cho Beom Pal) in charge and thought everything was going to be ok.