Re the comment about parents' observations not being as reliable as an objective assessment: this study used the well-known Strengths and Difficulties questionnnaire which has been validated as a tool and which has been used in many studies to get a consistent measure of behaviours seen by parents, so I think this should add weight to the study's findings.
Rita - this is a good point ie a certain 'type' of parent may be more likely to bf and have a different approach to behaviours. And it's this, not the feeding, that affects outcomes. This could be checked in smaller studies, I think.
You'd also have to rule out the possibility that breastfeeding 'teaches' parents a different approach! That is, you might start out with one idea, and find you change the longer you breastfeed. For example, you might begin as a routine-oriented parent with firm ideas on sleeping times and so on. You then find this does not work well with breastfeeding and you become less firm....and this affects other areas of your parenting, so you become more responsive and flexible, and this produces a child with fewer anxieties and stressors.
All this is speculative and may be rubbish - but it is a valid area of questioning!