I mean, strictly speaking, nothing in Darkrai's lore suggests that it can create illusions (only nightmares), and yet that whole "hotel that no one's been in for 50 years and yet still had a host who ushered you to sleep so you could teleport to Newmoon Island" thing still happened. Personally, I'd argue that Legendary Pokémon are powerful enough to have a free license to mysticism that the producers just don't feel like leaning into all that often.

Besides, you don't necessarily have to be dead in order to project your spirit.