Actually, I believe the character level does somewhat effect the generated stats - the higher the level, the better chance you have of getting stats in the upper range for that item.
In a game to try for the lowest level finish, Ariana reloaded a large number of times trying to get a holy weapon with Frost around level 5, but failed. Returning at around level 10, she found it much easier to get a better sword. She hit the gong on level 12 (ending up in the wastelands at 17), then quit.
