The answer is yes, but. Certainly, she should pay her fair share. The question is how to establish what is “fair” so that either (a) it is not challenged by Medicaid or (b) it can stand up to Medicaid’s questioning. You can either use your best judgment on the right amount, keeping careful records of the related expenses, or work with a local elder law attorney to determine the amount and how best to document it. The second route would be the safer course of action.
For more on Medicaid's asset transfer rules, read this article.