The $12,000 amount relates to the amount you can gift for federal purposes to avoid filing a gift tax return. Even if you make taxable gifts, there is no tax to pay until you make $1million in taxable gifts.
There is a separate 60 month rule with regard to eligibility for medicaid. It is true that the amounts can be factored in when determining when you may be eligible to take advantage of medicare.
It wouldn't hurt if the funds were retained in a special account in case that particular situation arises. This can be particularly important if you anticipate the need for that type of service within the next few years.