Was Rem's warning fake?


Rem warned Light not to hurt Misa or it would kill Light by writing his name
in it's Deathnote, but Ryuk had mentioned in the last episode as well as
before that either Ryuk would kill Light or that Light would die after living
his natural lifespan. As Ryuk has to kill him, was Rem's warning a bluff?

If so, couldn't Light, being a genius, see through his bluff??




Rem warned Light, but later Misa told Rem not to harm him, that she would
rather die first. So Rem, in order to preserve Misa's happiness,couldn't kill
him.

Light, being a genius, learned how to take advantage of the situation, and
used Rem on his plans, manipulating her like any other.

