It could be correct to use the comma, depending what the author means. The conjunction while can have two distinct meanings. One is “during the same time that” as in It’s never a good idea to inhale while your face is under water. The other meaning is close to “even though” or “but” as in Preferences in taste vary: my wife hates green beans, while I love them. A comma before while would be wrong in the former example, while it’s entirely appropriate in the latter.
And with your pair of sentences, the presence or absence of the comma could reflect which of those two meanings is intended.
And note that the second meaning—the one used to flag a contrast between its conjuncts—often has absolutely nothing to do with time. Consider The Framers of the US Constitution had fresh memories of monarchy and were attempting to prevent its ill effects, while today’s politicians seem so petty. The first group of people mentioned, the Framers, were all long dead before anyone in the second group was even born, so there cannot exist any moment during which they all were, are, or will be doing anything simultaneously.