No, it's neither mental gymnastics and you're factually wrong about the "power of Death" itself as a form or wavelength of magical energy. Death, both as a concept and as a primordial essence, didn't exist until the release of
Chronicle Vol. 1 - which came out in 2016, not 2002. Necromancers also predate the existence of the Lich King, as the orcs had
Necrolytes, who are themselves Necromancers, who could raise the dead as undead before Ner'zhul ever became the Lich King. Similarly, Gul'dan created the first generation of Death Knights before the Lich King existed as well. Scourge Necromancers do practice the same form of Necromancy as the Maldraxxi do, though; for all that matters to the discussion.
The context of Sin'dane's quote goes to show that Necromancy is not solely powered by the energies of Death and that no matter what energy gives rise to the undead, the principles of Necromancy remain the same. This is both literally and figuratively the meaning of her quote, impossible to either deny or ignore.
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No. Death Knights wield the power of Frost, Blood, and Unholy via runic magic. Paladins are directly infused by the Light and wield their power in the form of luminous and Holy-aspected magic. If a member of the Forsaken was made a Paladin, they'd be using very different abilities from a Death Knight (which Forsaken can already be).