It would seem that Elizabeth would have come up with a better cover story about hiring Vickie and why involve Roger. She could have just said a person who wishes to remain anonymous told her. Then when she thinks Joe knows "all the rest" she really loses it.
Maybe they were thinking about a Great Expectations storyline, with ECS as Mrs. Haversham! It seems to me after all the build-up and the implications about Liz being her mother, they'd feel obligated to go the other way, and have the benefactor be someone else, for some other reason. Or it could be the father sending the checks, with Liz or another woman as the mother. No one talks about who the father might be.