The money is always "taken out" by the account owner, not the beneficiary (unless the account owner is also the beneficiary, which is not the case in your assumption). The account owner specifies to whom the requested distribution goes: the beneficiary, an educational institution, or the account owner.
Under the quoted language you provide, if a Michigan taxpayer/MESP account owner who files as married filing jointly makes a $10,000 contribution to the MESP account and in the same tax year requests a $6,000 qualified MESP distribution to the beneficiary, the taxpayer/MESP account owner would be entitled to a $4,000 deduction from Michigan adjusted gross income for Michigan income tax purposes.