It is impossible to prove anything - it is impossible to prove the moon is not made of green cheese. Bringing back a piece of moon rock which is not green cheese is merely overwhelming evidence that it is not....it does not prove that the original green cheese it was made of has not transformed into rock, or that the lab which tests it has not made a mistake in its assessment blah blah blah.
You offered the statement 'there is no proof' [that bf is 'better'] as some sort of counter argument that bf is better than formula, and that all we have is a bunch of 'various statistics suggesting it is'. This is not a scientific argument. If we have to wait until we have 100 per cent proof, we will wait forever.
We have the next best thing, though. A bunch of 'various statistics' that continue to show, relentlessly, after controlling for variables, that the best health outcomes for babies come with breastfeeding....and the more breastfeeding, the more marked the difference (so a 'dose' response).
So - we have something that is biologically plausible (that species-specific milk adapted to the needs of the species, and promotes physiological norms ie better health) PLUS 'in vivo' evidence that this is indeed what occurs to real live human infants. I'd say that amounts to pretty solid evidence.
However, you 'personally believe' (in a very unscientific way :) ) that the difference is 'marginal'. I am not sure what population of babies, geographically or historically, you are referring to, but if we decide to be really parochial and only think about UK babies in the 21st century, we can observe that most babies grow well and are healthy, whether breastfed or formula fed, and whether breastfed for a long or a short time (which is absolutely not the case at every point in history or everywhere in the world even now). What we can't do is say any particular baby is 'marginally' affected, or seriously affected....even in the UK, even in the 21st century.