You're absolutely right; and there's no reason why you couldn't do what you did.
You're really only increasing their DPR by an average of 1 (per attack), so it's not the end of the world. It's no different than giving out a weapon that deals +1 damage, in that sense.
I've done something similar for a player who wanted to play a gnome ranger, but felt restricted by being a size category lower, and therefore unable to use a "heavy" longbow.
I made up a magic item, "the longbow of tying", which functioned like a longbow in terms of damage, but could be made smaller for a small player. Problem solved.