Because <PERSON>'s memory sequence was triggered by <PERSON>'s (played by <PERSON>) resemblance to <PERSON>. So while <PERSON> was in her coma, her Metaconscious used <PERSON> to represent <PERSON>. The memory sequence of <PERSON>'s death was stil within <PERSON>'s head, and <PERSON> did not yet know about <PERSON>, so <PERSON>'s image suddenly changing to a strange girl certainly would be confusing. Also, in-world, <PERSON> had not revealed the truth until then.
From the Wikipedia entry for the "Dark Page" episode, pertinent parts bolded:
<PERSON> returns to the Enterprise, this time as the teacher of an alien race learning to speak. Their native form of communication is telepathy, but they want to learn spoken language in order to interact with other races. <PERSON> comes aboard with <PERSON> and his young daughter, <PERSON>, who is <PERSON>'s star pupil.
Suspecting that <PERSON> is not her usual, flamboyant self, <PERSON> tries to investigate. When <PERSON> starts showing signs of fatigue, she is taken to Sick Bay to be examined. <PERSON> tells <PERSON> that her interaction with the aliens is more taxing on her telepathic glands than she is used to and is asked to refrain from telepathic contact with them until she can recover. <PERSON> helps her mother by verbally communicating with <PERSON> and <PERSON>, but <PERSON> still uses her telepathy when they don't grasp the verbal concepts. After an incident where <PERSON> falls into a pool of water in the arboretum, <PERSON> falls into a coma. With no signs of physical trauma, <PERSON> deduces that her telepathic abilities have caused her mind to collapse in on itself from the over use. <PERSON> uses his ability to form a bridge between <PERSON> and <PERSON>, and the former finds herself walking through corridors like on the Enterprise. 663
<PERSON>'s mental defenses pick up, first conjuring <PERSON>'s father to distract her, then an image of <PERSON> himself ordering her to sever her connection. She sees past these ruses and encounters <PERSON> petting a wolf, but the girl does not seem to know who "<PERSON>" is. <PERSON> then charges in screaming for <PERSON> to get away from her, causing <PERSON> to break her connection.
<PERSON> and <PERSON> search through <PERSON>'s things and find several pieces of the puzzle missing; journal entries for a journal <PERSON> kept since being married had blank pages from shortly after <PERSON>'s birth going on several years. The image of <PERSON> in her mother's mind does not add up. She tries again to reach her mother, this time, <PERSON> encounters the wolf by himself who chases after <PERSON> through the deck until she encounters a Turbo Lift that opens into space. Hearing her mother call for help, <PERSON> jumps in and lands in the arboretum where <PERSON> had collapsed. <PERSON> is there, still begging <PERSON> to leave, but <PERSON> refuses, stating that a repressed memory is killing her and she must relive the memory in order to survive. Suddenly, an image of a human girl who looks like <PERSON> is playing by the water with a puppy, and <PERSON> calls her <PERSON>. <PERSON> urges <PERSON> to relive what happened, and she tearfully remembers a tragedy when <PERSON> ran after the puppy when it got away, though it was unclear what had caused her death. <PERSON>'s repressed memory of <PERSON> and her resemblance to <PERSON> led to her coma. As <PERSON> recalls happier memories of <PERSON>, <PERSON> tells her to share them so she can learn about the sister she never knew. The women awaken in Sick Bay holding hands. 715