There is something to Boston Dynamics which makes them appear more credible than nearly anyone else:
1) They have chosen to build robots with really challenging mechanical... dynamics. The balancing actions they show cannot be faked with remote controls. They have to be truly autonomous features.
2) They are not just limited to stability of simple movements. Instead, they use their... dynamics very creatively in complex patterns. Again, can't be faked with remote controls (well, maybe except to give very high-level guidance, "do trick X now").
3) They demonstrated all of the above more than 5 years ago. From the current demonstrations the dynamics have not improved much, which is clearly because they were so impressive years ago already there is not much to improve. That very likely means they have been using their same engineering skills for something new, at a different level.
Besides, the demonstration they show in the video posted is not that impressive. I mean, if it was faked, they would have aimed higher. It is just right level of impression to be plausible.
There is a lot of "fake it until you make it" in robotics, and as such a lot of distorted expectations what can be and cannot be done. Having worked in a failed (seriously under-resourced and ran by... let's say unconventional opportunists) robotics startup some 5 years ago, I saw this pretty closely. Now when I see "autonomous projects" like delivery robots I'm nearly 100% sure they are at least assisted if not completely remote-controlled from some Indian call-center type cheap labor operation. It's not surprising Elon Musk does the same.
But I do believe that Boston Dynamics is one of the few who really fakes order of magnitude less than industry median. Possibly even near-zero faking.