J.B.
You are correct. Seeking help does not render oneself legally incompetent. Not only that...even if one is declared incompetent, that extends only so far and under very specific circumstances (for example, being able to check out of a clinic or change a will).
Becoming legally incompetent requires a court hearing. In my state, it's called a section 35. If someone were committed to a hospital or other facility, a person concerned about the patient can petition the court and present evidence that the patient is unable to care for him or herself without the patient being present and would need to present evidence of this. If the person were not committed to care somewhere, then the person in question would be present at the hearing.
At that point, if guardianship is granted, it would be either guardianship of the person (allowing the guardian to decide where the person lives and to direct medical care), guardianship of the estate (basically just financial and other decision such as wills) or general guardianship, which includes both.
Unless someone has gone to court and obtained guardianship of the person you are writing about, there is nothing invalid about her making decisions on her own behalf. Perhaps it would help her to have someone from the facility where she is staying explain this to her in a way that she understands.