It's true that while can sometimes be used "timelessly" to introduce a second clause that somehow "contradicts" the preceding clause (i.e. - while [on the other hand] = whereas = but = however).
As a native speaker I don't find OP's first example very idiomatic, but it's hard to explain exactly why. It's worth noting that I have no problem at all with what seems to be essentially the same construction...
Protons and electrons have equal and opposite charges, while neutrons are electrically neutral.
My gut feel is that my example is "okay" because the context is so clearly a timeless statement of "eternal truth" concerning two statements which are both (continuously, always) true, and which are mutually "contrastive, complementary".
This is subtly different to OP's context, where the second statement doesn't so much "complement, reflect" the first assertion - it flatly refutes, denies, contradicts it.
My advice would be to prefer whereas (or more commonly, but) rather than while in all similar contexts. That way you'll never actually be "wrong" (to me, at least; I accept that perhaps some native speakers would be happy with OP's usage as it stands).