As you correctly discerned, distinguishing the fetal cell free DNA from the mothers cell free DNA in the blood stream is one of the major challenges in this type of diagnostics.
Consequently, the results that can be directly linked to the paternal DNA are the most reliable.
In the case of the example you give, the high accuracy stems from the fact that in case of Monosomy X, there is no indication of neither a paternal Y nor a paternal X chromosome. While the Y chromosome is the most easily discerned, a paternal X chromosome could also be detected because in that case the cell free DNA would contain fragments of three distinct X chromosomes.
This publication summarizes the issue nicely:
Once the cell-free DNA fragments have been purified, small differences between the fetal and maternal DNA sequences are exploited in order to make a specific fetal diagnosis. To date, the majority of studies have focused on the detection of paternally inherited sequences that are entirely absent from the maternal genotype, such as those on the Y chromosome of male fetuses. This target is particularly attractive as it comprises a large portion of DNA which is not otherwise present in women.
Variable regions of repeated DNA (short tandem repeats or STRs) can be used to identify paternally inherited sequences, by comparing the number of repeats present with the paternal and maternal sequences. 29
Paternal alleles on the autosomal chromosomes can also be detected, if they are known to be absent in the maternal genome, but this requires detailed sequence knowledge of the paternal genotype of interest, as well as detection methods that can distinguish DNA sequences that might only differ by a single nucleotide. Importantly, all these methods rely upon the fetus inheriting a uniquely paternal sequence that is conveniently located for a particular diagnosis.
The reliability of these tests can apparently be improved by enriching the fetal cell free DNA:
Selective enrichment of fetal DNA, based on a difference in the average physical length of fetal and maternal DNA fragments, which can be exploited to increase the relative amount of cffDNA. Fetally derived DNA fragments are generally smaller than those that are maternally derived, being predominantly ,313 base-pairs in length (<PERSON> et al., 2004). Therefore, by using standard size fractionation to select only DNA fragments ,300 base-pairs, circulating cffDNA can be enriched such that it comprises around 70% of the total cellfree DNA (<PERSON> et al., 2004b), prior to detection and identification by either PCR (<PERSON> et al., 2005) or mass spectrometry (<PERSON> et al., 2006). 625