My Math-Fu is failing me

[RNightstalker]

You can only enchant masterwork weapons, and improvised weapons cannot be masterwork weapons.

I hate to do this but to his point, a masterwork arrow used to stab someone (Legolas was a big fan of it so it's got some precedent) would be a masterwork improvised, unless there's something specific that I don't know of. But to your point, just because anything can really be used as an improvised weapon, doesn't mean it's classified as a melee weapon. That's what makes the difference.