Rule 2.e. states:

"No person shall participate or vote in the nominating process for a Democratic presidential
candidate who also participates in the nominating processes of any other party for the
corresponding elections."

This rule does not require states to implement any specified process to assure that persons may not vote in both nominating processes, such as by consulting a list. Read it: it applies only to "persons," not to "states." If Michigan makes its best effort to comply with this DNC rule, for example by making people sign a statement saying they didn't vote in the GOP primary, there's no reason under the sun that this rule would bar them from conducting a primary that is fully compliant with DNC rules.