How can a regression model be any use if you don't know the function you are trying to get the paramters for?

I saw a piece of research that said that mothers who breast fed their children were less likely to suffer diabetes in later life. The research was from a survey of some 1000 mothers and controlled for miscellaneous factors and a loglinear model was used.

Now does this mean that they reckon all the factors that determine the likelihood of diabetes fir in a nice function (exponential presumably) that translates neatly into a linear model with logs and that whether the woman breast fed turned out to be statistically significant?

I'm missing something I'm sure but, how the hell do they know the model?

Thanks