There is a minor profile on the autosomal DNA of the bra clasp that is likely to be Mr. Sollecito's DNA; there is also a Y-Chromosomal profile that is likely to be his. One problem for the prosecution is that there are additional alleles in the autosomal profile and probably a total of three donors to the Y-chromosomal DNA profile. If some of the YSTR DNA was deposited in ways that were unrelated to the crime, then there is no reason to think differently with respect to Mr. Sollecito's DNA. The second major problem for the prosecution is that the bra clasp was collected about six weeks after the rest of the evidence, enhancing the possibility of transfers unrelated to the crime. The third problem is that the forensic workers stored the clasp improperly, making it impossible to retest. Why should one trust a lab that does not store evidence in a way to prevent microbial degradation? The fourth problem for the prosecution is that Raffaele was known to have been in contact with Meredith's door. If a forensic worker touched Mr. Sollecito's DNA then collected the bra clasp, this would be tertiary transfer. In the last fifteen years, the evidence for tertiary and higher order transfers of DNA has accumulated.
I don't have a fundamental objection to what Professor Balding and others have done, which is to create software to analyze complex autosomal mixtures, but there are specific issues that must be properly addressed in each case (I suggest reading some of Professor Dan Krane's writings on this subject if one is interested). Nor do I believe that his conclusion regarding the bra clasp was flawed, as I indicated above. But this sort of mixture analysis cannot make the problems that I discussed somehow disappear.
Now let us talk about one aspect of the DNA from the Mitchell case that relates to the issue of DNA mixtures. Dr. Balding was doing his work during the Knox/Sollecito case (a paper of his appeared circa 2013). TruAllele made its courtroom debut in 2009, although it is older. The DNA from Jodi's bra had at least three contributors and these were partial profiles. Given the state of art circa 2005, how was it possible to deconvolute a three-person (or more) mixture that was not even of full profiles? Without a specific and credible answer to this question, the claim that Luke's DNA was present is unsustainable.