No, Republicans cannot vote in the Massachusetts Democratic Primary. Only Independents and Democrats can. That at least makes some sense. Allowing Republicans to vote in Democratic contest, and vice-versa, is madness.
Right, but my point is that Romney apparently has no problem with voters supporting a candidate in the primary who they think will offer the weakest opposition to the candidate they really support. Romney is basically saying that when he was an Independent in MA, he was an Independent in name only (IINO?), and was actually supporting Republicans, but would sometimes vote for the weakest Dem possible in the primaries to help the Republican.
That's essentially what's happening in Michigan. Except you say that it's different because of the voter's party registration? (Actually, does Michigan even have party registration?) The voter motivation is identical either way.