No, no sarcasm meant. I had no idea whether this was true but was allowing for the possibility and was then just thinking out loud about the potential theoretical basis. I can't imagine that a headstand would make an actual difference in your weight for the purpose of a weigh-in, though I can imagine trace distinctions. I mean, people weigh up to a pound less on top of Mt Everest than they do at sea level because gravity isn't a constant. So I'm willing to at least imagine the possibility.
That said, you're right about the equal and opposite force with respect to my cup example, but I don't think that would hold true for the headstand example because a body is a contained unit. Better analogy is maybe a half-filled water balloon. If it was possible to weigh the balloon in a precise moment when the water was sloshing around, it would weigh less than it does when the water settles. No, blood and/or other bodily fluids don't work that way inside your body but maybe in some barely perceptible way they do.
I don't believe the theory I offered but don't think it was flatly idiotic either. Neither did the National Institute of Health, which did a thoroughly scientific debunking
here, abstract below, emphases mine: