There is a significant association between bed-sharing and infant death. An adult bed presents far more hazards of entrapment, suffocation and strangulation than a properly-designed crib or bassinet. I haven't seen the advert in question and can't comment on how accurately it conveys the evidence, but I think that it's absolutely right to strongly warn parents about the risks of bed-sharing.
If you think that it's disgusting for a government agency to try and save the lives of babies, that's your prerogative.
http://pediatrics.aappublications.org/content/early/2016/10/...
Now I have no idea if the number of cases was statistically meaningful enough to warrant action, compared to other public health risks. But I can sort of see why someone would be motivated to "do something", considering how devastating something like that must be, even compared to other accidental deaths of infants.
1. "Instead of killing yourself, why not call a suicide hotline?" I guess BART tracks see elevated levels of suicide. I don't really have much of a problem with this one.
2. "If you let your infant sleep in the bed with you, you are a bad parent." I have a problem with this. What a disgusting thing for the government to be doing.