I've noticed in two public dungeons today that the group boss / event does not award the achievement and skill point awards to characters. Bonesnap and Lions Den are affected. Can submit video -- This on on XBox platform.
Is it possible that you have already completed these achievements on another character? The AWA (Account Wide Achievements) now only give credit for the first time.
Khajiit Stamblade main
Dark Elf Magsorc
Redguard Stamina Dragonknight
Orc Stamplar PVP
Breton Magsorc PVP
Dark Elf Necromancer
Dark Elf Magden
Khajiit Stamblade
Khajiit Stamina Arcanist
Public dungeon / group bosses are tracked by which character has previously completed them, and the skill point is awarded to each character individually upon completion. Otherwise, we'd be creating a new character and would have a stack of skill points for each public dungeon group event a previous character had completed.
But you are correct in your note on the standard dungeons themselves. You walk up to a dungeon previously completed by another character and they shift to white / completed status instantly.