Tyler,
The biggest thing you are missing is the "look-back" provisions of Medicaid. If significant transfers have been made to others prior to applying for Medicaid, getting on Medicaid can be delayed for a significant period of time.
This is an arcane area and each state has somewhat regulations about transfers, etc. but it IS possible to make some transfers.
Some elder care attorneys, for instance, suggest creating a trust in which you claim no beneficial interest. Money can then be transferred to this trust on a monthly basis and accumulate there. Then, when the parents' assets are exhausted, they can apply for Medicaid and the trust can be used to pay for the many, many things that are not covered by Medicaid.
This is an extremely complicated area, full of traps. A visit to an elder care attorney would be a very wise next step. Failing to visit an elder care attorney would be very foolish.
Scott