Does Helm of Brilliance apply the bonus 1d6 fire damage on ranged weapon attacks?

Question

One of the members of my party argues that the bonus damage only applies on melee hits but based on my understanding as long as it hits disregarding what type of weapon. Just want to confirm this

Scenario:

Turn 1: Command word to activate blazing weapon

Turn 2: Attack with blazing hand crossbow dealing 1d6(weapon dmg)+1d6(HoB fire damage)+DEX

Answer 1

... When you hit with an attack using the blazing weapon, the target takes an extra 1d6 fire damage

You are correct. By RAW, the Helm of Brilliance does not distinguish from melee or ranged attacks, any hit will add fire damage.

But, as always, the DM has final say, take it up with him/her.