Can Medicaid make a claim?

This is the type of issue where you might want to consult with an Elder Law attorney. In some cases I've assisted clients transfer assets prior to the five year look back period. However, the rules are not the same in each state. The laws in your state may be different.
You see, Medicaid is a federal program, and the states may pass their own regulations, provided they come within the framework of federal guidelines and mandates. In some states the house is an exempt asset, and in others it is not. In my state, Pennsylvania, it is subject to estate recovery, with some exceptions. Again, you should find an elder law attorney and there are some listed in the directory at this web site. Pre-planning is perfectly legal; it is the same as taking a tax deduction. However, you want to do it in compliance with the law.

Check with your local Medicaid office. Show them the paperwork, have them tell you. You can't hide anything from them anyhow, so if you need an answer now, don't sit there guessing. Ask them.

Transfer of ownership upon the death of the parent, that sound like what is written in a Will. Since the parent still owned the house at the time of their death, I wouldn't be surprise if Medicaid could attach a lien on the property for repayment of the cost of caring for said parent.