It would be hard to study causality in this instance because of medical ethics. You cannot assign a treatment that you believe to be more likely to cause an infant to die, so RCTs are impossible in this domain.
http://www.medpagetoday.com/Pediatrics/GeneralPediatrics/164... -- co-sleeping babies are 21.7 times more likely to die from SIDS than non-co-sleeping babies, according to this study. That definitely doesn't prove causality. But the correlation is certainly waggling its eyebrows suggestively in causality's direction.
There are parents that co-sleep because they are disorganized, drunk, and so forth, not even able to put the children in their bed. That's the reason why probably there is no causality.
It's not a great argument necessarily, but people accept additional risk of injury to their kids all the time if the benefits outweigh the risks.