First, Tyson didn't claim that philosophy is not a productive contributor to our understanding of the natural world, but that for any individual, "if you are distracted by your questions so that you can’t move forward, you are not being a productive contributor to our understanding of the natural world." The latter is a much more defensible claim.
Next, it's worth quoting from the conclusion of the article defending philosophy against Hawking:
> No doubt there is a fair amount of ill-informed, obtuse, or ideologically angled philosophy that either refuses or tries but fails to engage with the concerns of present-day science. One can understand Hawking’s impatience – or downright exasperation – with some of the half-baked notions put around by refuseniks and would-be engageniks alike.
People justifiably take issue with some aspects of philosophy (postmodernism, for example, and its misuse of scientific terminology, as exposed in Bricmont & Sokal's Intellectual Impostors), and a few scientists certainly overshoot in their criticism, or make it unduly broad.
But I don't think it's accurate to claim that "today the 'public intellectuals' often say philosophy is outdated or useless".
Lastly, even if one thinks that philosophy is largely useless today, that doesn't imply at all that one considers "21st-century American values [...] the best, final ones, never to be questioned again".