For context, it’s a very clear Nazi Salute — and Musk did it more than once. The NYT is implying doubt because they’re afraid of losing access if they speak the truth and because some people who are financially dependent on Musk are denying what it was in public.
Did Jeff Bezos’ Washington Post mention it at all? The only thing I can find is “Elon Musk gives exuberat speech at inauguration”, a video which only shows part of it.