Tiberias was named so for the Roman Emperor Tiberius.
Jesus son of Saphat was "archon" of Tiberias (Vita 66, 134).
If Frans is right about Jesus son of Sapphias being the historical Jesus, then a possible mistake to put Jesus Christ under Pilate is the confusion between a chronological provenance (under Tiberius) and a temporal provenance (from Tiberias).
The archon of Tiberias was transposed chronologically under the archon Tiberius.
Why Pilate? Because of Tiberias.
Why Pilate? Because of Tiberias.
Nihil enim in speciem fallacius est quam prava religio. -Liv. xxxix. 16.