Actually, I believe that the answer can be found in
Unfinished Tales, in Narn i Hin Hurin. The following quote could explain this (emphasis mine).
Quote:
(Mim) '...But this I will add: he that loosed the shaft shall break his bow and his arrows and lay them at my son's feet; and he shall never take arrow nor bear bow again. If he does, he shall die by it. That curse I lay on him.'
Androg was afraid when he heard of this curse; and though he did so with great grudge, he broke his bow and his arrows and laid them at the dead Dwarf's feet. But as he came out from the chamber, he glanced evilly at Mim, and muttered: 'The curse of a Dwarf never dies, they say; but a Man's too may come home. May he die with a dart in his throat!'
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So I believe that Men can lay curses too.