Varro mentioned in this answer:
I think it's highly likely that originally Greek σσ had a distinct sound from σ which made it a closer match to a foreign [ʃ] than σ would have been, which is why it turns up in μεσσίας (and perhaps "Elissa"), but I have no reason to think the same applies to Latin.
I'd never heard of this before, but it would make sense with the transcriptions of messías and Elissa. On the other hand, we see Iēsous with a single sigma.
What is the consensus on this? Is there other evidence for σσ having a distinct sound? And if so, what might it have been?