Mr. Allen's position is carefully demarcated: He would like to see the decision "reinterpreted" to allow states to decide the legal status of abortion. Does that mean he would like to see it overturned? He won't say. So I suggest that Mr. Allen's "reinterpretation" would produce precisely the same result as overturning the ruling: States would decide the fate of abortion. I pause for a response. Nothing. I get more direct. "Why won't you say you want Roe reversed?"
I notice the same thing in a recent New York Times article:
Perhaps to demonstrate commitment, Mr. Allen recently became a co-sponsor of a constitutional amendment to ban same-sex marriage. He also opposes legislation classifying crimes against gay men and lesbians as hate crimes. When South Dakota passed a restrictive new abortion law, Mr. Allen said abortion should be left to the states — a view tantamount to calling for Roe v. Wade to be overturned.
But this is not actually true. It's simply false that such a 'reinterpretation' would produce precisely the same result as overturning the ruling; Roe v. Wade already explicitly recognizes the authority of states to take measures to protect prenatal life, as anyone who has read the decision knows. What it does is balance against this the right to privacy, so that the right to privacy overbalances the authority of state interest earlier in the term, and the authority of state interest grows stronger as the term progresses. As the decision explicitly says:
...it is reasonable and appropriate for a State to decide that at some point in time another interest, that of health of the mother or that of potential human life, becomes significantly involved.
And again:
The decision leaves the State free to place increasing restrictions on abortion as the period of pregnancy lengthens, so long as those restrictions are tailored to the recognized state interests.
This has usually been understood, both within this decision and afterward, to mean that prior to viability state interests cannot be sufficiently strong for restriction of aborition. Overturning Roe v. Wade would mean overturning this balancing (which was explicitly reaffirmed by Planned Parenthood v. Casey). Allen's reinterpreted Roe v. Wade, which is actually a very common libertarian position, would have to take this balancing strictly -- the state, not the federal government, would have jurisdiction in this matter, and the laws passed by the state would have to recognize this sliding movement, whereby the state's interest is very weak toward the beginning of the term and stronger toward the end (I don't know if Allen would accept the point about viability). Federal laws concerning abortion, whether one way or another, would not be allowed; states would be allowed discretion so long as they show that state interest is involved and significant.
On Allen's own position, in interviews (e.g., here) he always puts the emphasis on the claim that "the people in the states ought to be making these decisions" and shrugs off the question of whether this should be considered an overturning of Roe v. Wade or not. But there's nothing in the position that requires the overturning of Roe v. Wade, which already explicitly affirms that states have some authority in the matter, and says nothing about the federal government. (This is not to say that I think Allen particularly consistent in general on this subject; I'm not sure how he would go about reconciling his voting record with his stated position, for instance. But there is nothing inconsistent about leaving it to the states and not overturning the decision.)
So there is a possibility that opinion journalists appear to be systematically misrepresenting: the states should decide because the federal government can't be said to have sufficient interest in the matter (abortion as such is not an inter-state health issue, but an intra-state one). The only role of the federal government would be the judicial one of guaranteeing both that the state laws take adequate steps to protect relevant rights and that discretion about such laws remains entirely at the state level. This, however, is entirely consistent with Roe v. Wade.
It's also the way we do most things most of the time, at least in theory, although in practice it's more complicated.