How does sample size help at all with that problem
Telling someone to only think about something in particular is a LOT different than telling them to take a pill a certain way.
It's simply not comparable.
True, but that's why you carefully define what to tell them to think about. Survey questions go through rigorous revisions until they express the exact idea that the experimenter wants to.
This is really the same thing. No good researcher is going to say "think about the color red". It's more likely to say something like "Imagine a solid, texture-less, shadeless, red wall that matches the red color you see in this picture"
Secondly, the larger the sample size, the more data you have. It's easier to find a common pattern that way.
Your assumption seems to be that if I say "imagine the picture that I'm holding up" that every single person in the world is going to have absolutely no common pattern. So far I haven't seen any indication that this is false. On the contrary, we seem to be very similar in how our brains think. It's complex but there are many common patterns, especially in the less complex areas such as motor control, optics, ect...