Are berries acidic enough they must be on top, not within, panna cotta?
Reporting experimental results.

I hypothesized that frozen berries will fare better than fresh. The reasoning? It will take them a while to thaw if the cream is poured at room temperature and put in the fridge right after. By the time they thaw, the cream would have set.

In practice, it's more complicated. Alchimista's hunch is accurate. The skin of the berries is not as impermeable as one would think (I skipped strawberries, since they're inherently porous).

Perhaps the berries will keep just as well inside as outside; that is not entirely clear. But the cream will not set as well near the surface of the berries as it sets farther away, and soggy panna cotta seems like a candidate for going bad sooner.

All in all, I'd say keeping the berries on top is a better option. Besides, an enhanced presentation is a good attribute for homemade desserts as well.