Considering people including myself have successfully beaten the game(s) using a Lvl 1 character that never upgraded his stats, I find this statement dubious 
(thou I suppose there could still be some token grinding for the weapon upgrade shards, but then again since in that kind of run you’re not spending souls to level you might as well buy them in bulk)
Honestly, few of the DS bosses are really unfair or comple bullshit. The Bed of Chaos and Smough/Orstein in 1 ; Royal Rat Authority, Old Iron King and maybe the Rotten in 2 ; Aldrich & Nameless King in 3 are the only ones that can really destroy you for bullshit reasons (two of those bosses are optional, too).
You could add a few more to the list who have obscure gimmicks, like Mytha Baleful Queen in 2 or the Deacons of the Deep in 3 ; but once you *have *heard about their gimmicks they become quite easy. Oh, and the first meeting with Seath in 1 - a mandatory death in a game where death makes you lose so much is pretty unforgivable and I’m glad the devs never repeated that “hilarious” little prank. But again, once you know it’s coming it’s easy to just put on a sacrifice ring before setting foot inside the room.
Every other boss *can *be clowned on your first few tries if you’re playing carefully and mind your surroundings, even playing blind.