Quest items, just like keys, potions, scrolls, etc. have ilvl 0 and their ilvl has no incidence on anything.
So yeah it’s a myth.
You can test it easily by using some super specific low lvl formula at a breaking point where +1 to ilvl or clvl wouldn’t make the result possible, but it still works.
Thanks, had to ask since I play SP / P8 D2LoD using D2SE and it shows ilvl of all items, and the cube has different ilvl per difficulty. The runes have ilvl 0 etc.
D2:R