There are a few quirks of the damage type system that are not currently displayed to the user as I've yet to come up with a neat way to do it.
One of these quirks is that the DoT component of skills such as Explosive Shot do benefit of the Damage Over Time stat. The DoT component of these skills is also not included in the Damage Per Second or Average Damage calculations just yet. Though the new Damage Meter will correctly record the damage dealt.
Another one is that all Offensive Cooldowns will gain the damage type of your main weapon. So in your case Pin Down will scale with Ranged Damage in addition to it's listed damage types.
In all other cases if a damage type is not listed then it will not apply.