The primary SIDS risk factors are not putting the baby on its back, smoking in pregnancy or around the baby, and breastfeeding for less than two weeks, according to what I've been told. These factors are more likely to be present in very low-income households, with less contact with HCP and information on child safety. Therefore a higher risk in those infants is explicable without poverty being a causal factor in itself.
Since Back To Sleep started, cot deaths have been cut by 70%. Given that also coincides with the widespread use of grobags (they're safer in terms of suffocation risk avoidance, plus the baby can't kick them off and waken when cold) it just isn't possible that the reduction is because babies can kick covers off when lying on their backs and thus not overheat. It has to have something key to do with the sleeping position itself. No other explanation holds up. Overheating may be a risk, co-sleeping, separate rooms, not using a dummy, and so on. But given the huge reductions since the sleep position/smoke risks were made known, they can't be the primary causes. The 70% reduction means that's already been identified, surely?
To be honest I'm amazed if anyone still puts a newborn on their fronts. I had this argument with my MIL who just can't accept what she was told was wrong, and insists front is safer - I appreciate it's horrible to be told something you did in good faith for the benefit of your baby is actually more dangerous, but I suspect every generation will have to grapple with something along those lines. Several kids with serious nut allergies may have them partly because their conscientious mums followed the advice at the time to avoid all nuts in pregnancy.
All I know is that for every 3 babies who now die of SIDS, 7 don't, and it's largely attributable to Back to Sleep. I for one am bloody grateful for the info.