In terms of constitutional originalism, she's....well, possibly wrong. In terms of contemporary twenty-first century American culture and politics, she's absolutely right. Guess which one is more relevant today?:
CHUCK TODD: “When, or if, does an unborn child have constitutional rights?”
[MRS.] CLINTON: “Well, under our laws currently, that is not something that exists.. The unborn person doesn’t have constitutional rights. Now, that doesn’t mean that we don’t do everything we possibly can, in the vast majority of instances to, you know, help a mother who is carrying a child and wants to make sure that child will be healthy, to have appropriate medical support. It doesn’t mean that you don’t do everything possible to try to fulfill your obligations. But it does include sacrificing the woman’s right to make decisions. And I think that’s an important distinction, that under Roe v. Wade we’ve had enshrined under our Constitution.”
Is the Empress constitutionally right or wrong about that assertion? Essentially....yes.
It gets into the wording of Amendment XIV, Section 1:
Section 1. All persons born or naturalized in the United States and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws. [emphases added]
With the understanding that when the Fourteenth Amendment was written a century and a half ago, nobody imagined that murder of the unborn would become not just a major national industry but be illegally enshrined as an inviolable, sacrosanct constitutional right, the question is the distinction between "all persons born in the United States and subject to the jurisdiction thereof" and "any person". The former (born to two U.S. citizen parents) are designated protected citizens of the United States and their particular State, whereas the latter is (1) a larger category than just citizens and (2) are also accorded the same equal protections, including of their lives.
The logical take-away from that paragraph is that the Equal Protection Clause is not limited to citizens, but to "any persons". Would the unborn child not reside in that category? They are (1) alive and (2) human, and therefore "persons" by any measure. The problem is that that is not explicitly enumerated in the Constitution or any of its Amendments. Which should, on the one hand, have rendered it a State-level issue be definition via Amendment X, and did, on the other hand, leave a truck-sized opening for Justice William Brennan to "discover" the "right" to abortion of which Herself is so hardcore fond.
The options are pretty cut and dried: (1) The blood-soaked status quo; (2) a Human Life Amendment, which has zero chance of ever being passed, let alone ratified; (3) State-by-State nullification via reassertion of Original Authority, which has little more chance of succeeding than the HLA; or (4) figure out a naturalization process for the unborn, which would be problematic given that they would have to take a test and an oath.
So, to sum up, Hillary Clinton shouldn't be right that "unborn children have no constitutional rights," but while you can't say that she is, it is incontrovertible that those of her view hold all the power cards.
Or maybe I should say all the "trump" cards, since The Donald's latest attempt at articulating a position on abortion stated pretty much the same thing, only a lot less coherently.