I'm wondering if it's really the framing of the problem that's inflating the number of individuals responding with blue (similar to certain confusingly-worded ballot measures).
Suppose the problem were worded in a more concrete way: "I have a large container ship that I'm draining the ballasts out of tomorrow. If less than 50% of <whatever population we're working with> get on the ship, it will capsize and everyone who chose to get on it will die. You can choose either to get on the ship (blue button) or refuse to (red button)."
Would one hold a person guilty for not getting on the ship? Would a perfectly empathetic person even board that ship?
Of course the framing affects how people vote. The thought experiment demands we use the framing as given. Some people might reason themselves into your analogy, others won’t.