It's the most counter-intuitive thing in the world that rand() rand() is less secure than rand(); shouldn't it be twice as unpredictable?*

Under some reasonable assumptions, rand() + rand() mod 1 is twice as random! If both calls return independent samples, and at least one of the calls to rand() returns a uniform sample in [0,1], then the sum will be uniform on [0,1].

So if you assume you get at least one good shot and that the other is not specifically correlated to it, you'll be improving your randomness.