Another sort of character might be offended at Miss Woodhouse's impertinence - but Harriet is more like a simple Maria Lucas than a witty Miss Bennet.
Indeed, her ductility,"only desiring to be guided by any one she looked up to", is one of Harriet's most powerful charms. Emma could hardly suppose herself a useful acquaintance, otherwise.
"She was ready to tell every thing in her power" but ""She had been satisfied to hear and believe just what Mrs. Goddard chose to tell her; and looked no farther." And now, she is satisfied to hear and believe just what Miss Woodhouse chooses to tell her.