My MIL has been living in assisted living. We have applied for Medicaid several times and finally have been approved. Can anyone help me understand?

She has been living in assisted living since Feb 17. They told us that Medicaid will start July 1, 2018. It will not pay back to Feb 17, 2018. Furthermore, her house was appraised for 69,000.00 and sold for her mortgage payoff which was 65,088.00. Medicaid told us that beginning July 1, 2018 and until we make up the appraised value of 69,000.00 they will not pay anything either. So they are not paying from Feb 17, 2018 until July 1, and they are not paying the first 69,000.00 from July 1. How do I fight this when we sold her house for 65,088. The bank informed us that we were close enough to the appraisal value to be ok with Medicaid. I am so disgusted right now. Can any body help me understand or make a suggestion?