And their mothers, assuming they were between 13 and 50 when they gave birth, would therefore have been born between 1850 and 2010.

So that's 161 out of 9999 available last-4's (0000 is not used) that could possibly be someone's mother's birth year.

And then, of course, it has to be the right year within that space.

I am guessing this was something that happened to a few folks by chance and then was blown up by people who don't understand how many coincidences can occur across a population of millions.