You seem quite fixated upon probabilities. While this can be an interesting pastime, you are conveniently brushing aside the statements which clearly prove that secondary transfer is a reality and one which can account for the DNA in this case.
Sometimes the transfer is so small because of the shedding characteristics of the people being tested that no profile or only a partial profile can be obtained.
Conversely, it has also been shown that the major profile from a sample can be obtained as a consequence of secondary transfer.
The relevant portion of the article is:
The strongest profile obtained was not always that of the person who last held the object, but was dependent on the individual. We regularly observed profiles of previous holders of a tube from swabs of hands involved in these exchanges, showing that in some cases material from which DNA can be retrieved is transferred from object to hand (secondary transfer).
http://www.bioforensics.com/conference07/Transfer/SecondaryTransferStudy.pdf
titled Secondary transfer study Henry Lee co-author,
"If secondary DNA transfer is, in fact, a realistic possibility under field conditions, that may have signifi- cant repercussions for DNA testing in criminal investigations.
Given its importance, we have systematically studied the issue of secondary transfer in an attempt to evaluate the findings of van Oorschot and Jones and their relevance to casework. Since the au- thors specific methodology was not reported, we were unable to duplicate their experiments exactly. Therefore, we tested a series of conditions where detectable secondary transfer might occur. The study addressed situations that might realistically be encountered in field situations or at crime scenes."
"Two possible modes of secondary transfer were considered: (1) skin to skin to object (handshaking) and (2) skin to object to skin. For the first scenario, objects were pre-cleaned with 10% bleach and wiped with 95% ethanol. Subsequently, laboratory personnel shook hands for various lengths of time (1, 5, 10, 30, 60) and then held the pre-cleaned objects for 5 s (Table 1). The handshak- ing and handling of objects were not static. Palms were rubbed against each other or against the object to promote maximum DNA transfer. The individuals palms or the handled objects were swabbed with moistened (dH2O) sterile swabs. For the second mode, coffee mugs (Table 2) were handled per regular usage over
2 h and then handled by a second individual for 10 s."
"With respect to secondary transfer, peaks above back- ground (1520 RFU) f
rom the second individual were not detected for most STR amplifications. On occasion, minor peaks (below 75
RFU) from the second individual were observed. However, in these instances, allele dropout was routine. The complete sec- ondary profile was never detected, even if the data were analyzed in the 5075 RFU range. It should also be noted that, generally, amplification would not be attempted on many of the experimen- tal samples we tested since the manufacturer recommends using a minimum of 250 pg (35 cells) of DNA template for PCR.
Our data indicate that the primary transfer of DNA by handling
is possible, but detecting an interpretable genotype is not assured. Secondary transfer was not observed under our experimental con- ditions. Therefore, our data do not support the inference that the in- terpretation of DNA profiles from case samples could be compro- mised by secondary transfer.
Both the paper you cited and this paper is clear: primary transfer is much more likely than secondary transfer and more reliable.
