Did the Alito Opinion Leak Change Roberts' Vote?

Interesting fact.
Roberts voted to sustain the Miss. law. That means he assigned the Opinion to Alito. He certainly knew what Alito was likely to write. And he ended up not joining the opinion, only the outcome.

I'm going to guess he wasn't originally with the majority.

— Shipwreckedcrew.substack.com (@shipwreckedcrew) June 26, 2022

Maybe the leak of Alito's draft opinion encouraged Roberts to join the conservative majority to put an exclamation point on the decision. After all, the Chief Justice did say, "To the extent this betrayal of the confidences of the Court was intended to undermine the integrity of our operations, it will not succeed. The work of the Court will not be affected in any way." 

And then, by assigning the opinion to Alito he straddled the fence, upholding the Mississippi law, while at the same time saying he wouldn't have struck down Roe v. Wade.