Understanding recombination scoring in family pedigrees
Ns are not non-recombinant at the genomic level. What you know is that they do not show recombination events at the risk allele locus as subjects carrying the marker A1 show signs of the disease and similarly healthy subject do not carry the marker A1. Hence they are called non-recombinant. On top of that 3rd generation subjects (excepted III6) show combinations of alleles reflecting inheritance of one allele from each parent.

What is very important is that A1 is not the allele, it is the marker for the risk allele. This means that A1 is not directly the allele but a region of DNA close to the allele provoking the disease, sufficiently close to be co-inherited most of the time with the disease allele.

For III6 you actually know that a recombination must have happened as this subject obviously carry the risk allele (shows the disease) yet not the marker associated with it, therefore a recombination event happened between the marker and the disease allele.