The second boil also ensures a good seal on the jars. The thought is that the jars/lids cool some during the filling and may not seal as well. In addition, the second boil is intended to kill any germs introduced during the fill process.
We lived in the UK for nine years. I was always surprised how common it seemed for people to reuse product jars and lids for their canning, often using a paraffin layer directly on top of the canned jams, etc. In the States it seems more common to use two-part canning lids and heavier glass canning jars. But I ate plenty of home-canned things in the UK and never got sick and developed a love for quince jam!