Dori text: "Response: After a hero is assigned any amount of damage, exhaust Dori to place that damage on Dori instead."

Technically, this text does not target any other card: it simply moves damage.

But Beorn text is: "Sentinel. Cannot have attachments. Immune to player card effects. Beorn does not exhaust to defend. "

What do you think?

Yes, Dori can siphon damage away from Beorn. Caleb Grace of FFG recently clarified this interaction, citing the same point (targeting damage rather than the character) that you mentioned.