I'd heard that Warren Burger would pull this trick
But here's the proof, from Justice Brennan's notes of a conference of the Justices on Ballew v. Georgia in 1978. Issue is -- the Court had earlier held that criminal juries can be as small as six jurors, but Georgia went to five.
Chief Justice Burger starts out "The figure of five versus six doesn't bother me--I can't see how there is a constitutional issue." The other Justices state their votes, and it's obvious that position loses. Burget ends with "I change my vote to reverse on the five-man jury. Five is constitutionally inadequate."
The trick -- the Chief Justice writes the opinion, or assigns it out, only if he is in the majority; otherwise the most senior Justice in the majority assigns it. By changing his vote, Burger puts himself in the majority again. It's interesting that Blackmun, sometimes called his twin, switches also. Surprise! Burger assigned the opinion to Blackmun.