End of the day, the rules don't differentiate between a close burst 1 done with a weapon in a melee style or a thrown/ranged style. For example, if a rogue with a dagger does a close burst he might be stabbing or throwing his dagger, or even both.
It's probably not the most logical line of argument. You're far better off trying to compare items to other items.
I do actually agree that these items should not be included in any campaign as they're far better than their alternatives, in any of secondary slots, or indeed almost any alternative after a weapon with a higher +...
There's actually a really problematic gap at the moment between items with passive effects and those with, say, daily uses. Eh well.
Iron armbands only work if you don't use a shield. So you're giving up +2 ac and +2 Reflex for +2 damage per tier, as well as whatever other useful goodies there are on the shield if it's magical.