I'm sitting here looking at that image and it suddenly dawned on me that St. Peter is wearing a mini-version of the triple tiara...
From Fr. Selvester:
One sad nod to the present state of things is the lack of the tiara on the statue of St. Peter in the basilica. On this feast the statue is vested in papal vestments that used to include the tiara as well. Since the Popes no longer wear the tiara it is missing on the statue too. The custom was maintained during the previous pontificate but it is another Marini innovation. Oddly, though, the statue was bare-headed. If they're going to continue to vest the statue one would think they'd use a mitre as the Popes do now. Some would argue that St. Peter would have worn nothing on his head. True enough, but then again he wouldn't have worn a renaissance cope either, or a ring, or a pectoral cross, or a morse or had a visible halo. Since all those are used then a mitre to replace the tiara would make the most sense. Otherwise, why vest the statue at all?