It's really all about the DNA sequence testing. The sequence of DNA is very specific and if that particular sequence is missing then there is definite illegitimacy.
There have only been five people so far who tested, and they fall into two haplogroups, R1 and I1. R1 is a huge group, and only if the particular R1 DNA sequence is not there it means illegitimacy. One really has to find descendants from earlier off-shoots of a family line to compare their DNA to yours. A comparison of older lines in the same family and the newer lines should show whether or not there was illegitimacy at some point.
I thought my DNA test might show that I was illegitimate, but I have the exact same DNA as my second cousin, so we are both descended from a common male ancestor. What we would have to do is find another male from a line that branched off even further back and see if the exact haplogroup DNA sequence shows up for him as well. If this more distant cousin has the same DNA sequence then the odds are the line is not illegitimate.
Surnames mostly began in the late 1400's, so it would be difficult to prove illegitimacy before the use of surnames, because surnames are a form of general identity showing a relationship between people with the same surname. Therefore it is surprising that some Windsors are R1 and some are I1, haplogroups which branched off from a common ancestor about 25,000 years ago. This means probably the name Windsor was not just for descendants of a common person, but rather a name that became used as a surname by different people who were not related.
If most of a Windsor line is, for example, I1, and suddenly a member of that family came up C or R1 haplgroup, then certainly that change would mean illegitimacy.
I hope this is not overly difficult to understand.