Strange Curses!

[Nilpaurion Felagund]

It had been held lawful only for the King of Númenor to call Eru to witness, and then only on the most grave and solemn occasions. The line of the Kings came to an end in Ar-Pharazôn who perished in the Downfall; but Elendil Voronda was descended from Tar-Elendil the fourth King, and was held to be the rightful lord of the Faithful, who had taken no part in the rebellion of the Kings and had been preserved from destruction. (UT III 2 - endnote 44)

Perhaps the people of the King of the Mountains had sworn an oath not dissimilar to the one sworn by Éorl to Cirion. And since both Isildur and Cirion called Eru in witness, any effects of those oaths will be upheld by Eru.