The randomized experiment you did is so cool! I love experiments like this -- like the Allais Paradox -- that reveal biases and irrationalities.
But in this case, as a game theorist, I aver that the switchers are correct. This is a classic application of Schelling points. If we all have the altruistic utility function "minimize death" then there are two Nash equilibria: (1) Everyone take the pill, and (2) no one take the pill. If the question is framed such that everyone taking the pill (like when it's just pressing one of two buttons) is focal, that's the equilibrium you expect and the one you rationally adopt yourself. When it's framed the other way, you expect the other equilibrium and rationally don't take the pill.
PS: I just realized that this is also the exact problem you called out in encouraging us to get set up on kbin for comments. The two equilibria are "no one else is going to set up an account so I won't bother to either" and "that's the new Schelling point for Dynomight comments so of course I want to be there too!"
PPS: Taking you up on your self-promotion encouragement, I predict that Dynomight readers will like the Beeminder blog, maybe especially the posts tagged "rationality". (Also I'm excited to see some of you at Less Online!)
Fighting me and other survey results (dynomight.net)
Do extroverts have more martial confidence?