I'm confused...

If a group of people, from prehistory, believe something to be true (having X will make you feel Y) and that belief affects their behaviour (when they get X, they feel Y - like a placebo - although some who do get X do not feel Y - but they are the minority), then when scientific studies are conducted (by rational members of the same group) into the effects of X on behaviour Y,  it should yield results that X is strongly correlated with Y (there is no control group, everyone is exposed to the same belief and social pressure that reinforces that belief).

What will a rational member of that group conclude about the effects of x on y? How can you rationally correct for bias if there is no control?