Yes, she's a nurse. Not a very good one apparently. And i too think that Moe took his job seriously. But the thing that made me think that Lizarde was on to something was the HKS blackmail factor. "Come on Moe, try this. We're at home. You don't have to worry. No one will know. Come on Anna, tell him it's ok.".
I think it wouldn't take much for Moe to crumble, he had an obvious crush on ANS (remember it was he who went to the hospital with her, not HKS) and he and HKS had a huge argument and falling out over the camera at the gravesite and in the church; I don't think they are buddies these days.