Note that spreading the idea that the transmission rate of AIDS is low has negative utility, regardless of whether it's true or not, since it would encourage dangerous behavior.
This is untrue. Consider a similar claim: "spreading the idea that very few passengers on planes are killed by terrorists has negative utility, regardless of whether it is true or not, since it would encourage dangerous behavior."
Informing people of the true risks of any activity will not in general have negative utility. If you believe a particular case is an exception you need to explain in detail why you believe this to be so.
In the case of infectious diseases, there are large unpriced negative externalities involved. Everyone doing what is individually rational, given true beliefs about transmission rates, is likely not socially optimal, because the expected individual cost of a risky action is less than the expected social cost. Giving people false beliefs about transmission rates can improve social welfare by shifting the expected individual cost closer to the expected social cost.
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