Hillary Clinton actually said...

The New START treaty positions the United States to continue its international leadership role in advancing the goals of the NPT regime.

Extended nuclear deterrence will remain strong under the New START treaty, including for those within range of Russian tactical nuclear weap...

The New START treaty does not constrain the United States from developing and deploying the most effective missile defenses possible.

The unilateral statements are not integral parts of the treaty, and they are not legally binding.