Harriet is so eager to please Miss Woodhouse, and so artless, that I can't see her concealing anything from Emma that Emma wanted to know.

Harriet has been raised to be comfortable but aware of her insignificance. If she had ever asked who her family were she was probably told that she couldn't know & that was that. Emma can't imagine being satisfied with so little information--but she can't imagine what life is really like for Harriet.