I used to work in the escrow department of a mortgage company and managed the tax files for customers. Michigan is on the higher end of property tax rates along with other upper Midwest states like Wisconsin and Minnesota. I'm assuming their home is quite expensive and has a high assessed value. I've found Illinois to not be any higher than Michigan when given similar taxable values.
Contrast to popular belief, California is actually pretty low on property tax. Their tax rate is only around 1% but the taxable value on homes is so much higher. You would pay roughly double in property tax on a similarly assessed house in Michigan. Texas is another state I was surprised by how high the property tax was given their lack of regulations and terrible power grid.