My scattered thoughts, as a scientist and breastfeeding mom:
I agree that the scientific evidence on breastfeeding health benefits is overhyped. The science is just not nearly as strong as some of the rhetoric.
However, just because there is some overselling, that doesn't mean that benefits do not exist. Absence of proof is not proof of absence. And, as Red Pyjama noted, the inclusion criteria for a given study can play a major role in influencing the outcomes. Once you roll a bunch of studies (mostly observational, some experimental) into a meta-analysis, the waters get pretty muddy.
One of my personal favourite overview charts on the epidemiology of breastfeeding is this one:
http://i23.photobucket.com/albums/b3...fits_bfing.jpg
It's beginning to be a little out of date at this point, but I think it nicely makes the point that there are different levels of evidence -- some statements have more weight behind them than others.
Strong scientific evidence is difficult to come by in this context partly because there are only a rare few situations in which you can run a randomized controlled trial on breastfeeding. (And you're certainly never going to get a double-blinded study. Most women can tell whether or not they are nursing.

) Even for cohort studies (prospective or retrospective), until you get significant numbers of women breastfeeding to the recommended age, it can be difficult (read: the research gets more and more expensive) to get sufficient sample size to really dig into the results of following those recommendations.
I notice when the science around breastfeeding is overhyped. Although I recognize that there may be some good reasons for this (e.g., lactivism is going up against some very powerful financial interests and discouraging social norms) my concern about the overselling is that it can lead to people rejecting the science entirely. If you make it sound like babies who are not breastfed are doomed to illness, anyone with a brain can look around and note that that is just not true. Some people respond to that by then deciding that there is no meaningful difference at all. It's really difficult to talk about small probabilities in a way that emphasizes a large relative risk (e.g., twice the chances of XYZ) but also acknowledges a small base risk/natural frequency (e.g., 2 in ten thousand vs. 1 in ten thousand.)
So I get the concern. However, I personally find even the limited 'strong' evidence fairly compelling, and because I am very aware of the limitations of science, I recognize that some systems are complex enough that they do not lend themselves well to standard methodology. Every day, we get more and more evidence that hey, when you take a complex system and start mucking around with it, you get unintended consequences. I don't think that nature is benign, but I have a healthy respect for nature, and as a mammal, that's one of the many reasons I am still nursing my 3 y.o.
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Note 1: When I say 'the science' or 'scientific evidence' I'm really talking about the epidemiology, because as far as I can tell as a non-bench scientist, the biology and microbiology on this question are pretty darn strong.
Note 2: Type 1 diabetes was mentioned in the article by Kramer as one of the things for which there isn't much evidence to suggest that breastfeeding is protective. In that case, as in many others, I imagine, there will be more data coming. It will be worth watching to see the results that come out of TRIGR, a 10 year, multicentre trial looking at the environmental triggers for type 1. They strongly encourage exclusive breastfeeding to six months, but for moms who don't breastfeed, switch to formula, or supplement, they are randomizing babies to either standard formula or a formula with the cow's milk proteins broken down. So in the end, they should be able to do a comparison of exclusively breastfed babies and both types of formula (observational), as well as comparing the two types of formula (RCT.) I am not 100% sure, but I believe that the trial is fully enrolled now and they're just waiting for all the kids to reach age 10.