I agree that statistics have to be interpreted intelligently - that does not mean making preposterous assertions such as 'my kids are fine and I bottle fed and my sister's are breastfed have asthma so there, that proves it's all rubbish'....not accusing anyone here of saying that, especially, but personal experience does not negate proper studies.
You will never be able to show that formula feeding directly causes increased mortality in the developed world to the standard asked here, because you can never do a randomised double-blind controlled trial, where you assign 1000 mothers to feed one way and 1000 perfectly-matched mothers to feed another, without the researchers or the mothers knowing who is doing what This is of course the way pills are tested, with placebos compared with active pills.
The research published in the Washington Post certainly does not mean 'you could correlate it to anything' because they do have an explanation for some of the excess mortality - the known facts, as they say, that formula fed babies have more infections and are more likely to die from SIDS. What they haven't done is to control for social and economic factors, but because the study looked at so many baby deaths, the sheer power of numbers does go some way to give weight to their results.
And the physical proximity argument is not saying that formula feeding mothers are less concerned about safety or feed at a distance - for goodness sake! It is, as I understand it, a reflection of the fact that breastfed babies do tend to feed more often and are therefore probably held more often, and are less often in a situation where an accident might befall them....now in any individual situation, you cannot quantify this, but when you have very many babies in a study, this might act as a perfectly rational exlanation for some of the excess mortality.
I don't see the importance of the distinction between there being 'something wrong with the formula' (in GdiG's words) and which therefore causes excesss mortality, and the whole experience of feeding. Feeding is more than just the action of getting milk into a baby. It is a complex act, a relationship, and all the circumstances of it should be taken into account when studying its effects. This means, of course, you won't get simple answers that say 'Magic ingredient X is not present in formula, and Horrid ingredient Y is, so that's why formula causes excess mortality'. Even then, is it the absence of X, or the presence of Y that's to 'blame'??
No - we won't get those simple answers ever - you are stuck with epidemiological research, backed up with smaller studies that look at the constituents of breastmilk or formula milk. So we end up with complex answers, which nevertheless have a clear result, showing that excess mortality in babies who are not breastfed.