The D-statistic takes the form:
D(H1, H2, Vindija, Chimp) = (sum of ABBA - sum of BABA) / (sum ABBA + sum BABA)
If A: chimp allele, and Vindija (the Neandertal source of the "Neandertal genome") has the derived B allele, then in sites where two individuals H1 and H2 differ, there are two possible patterns:
ABBA = H2 matches Neandertal, but H1 does not
BABA = H1 matches Neandertal, but H2 does not
If Neandertal did not contribute DNA more to H1 or to H2, then the rates at which ABBA and BABA occur are equal, and the D-statistic has an expected value of 0.
Now, consider that H1 is a living human, and H2 is one that lived X years ago. It is now not expected, that ABBA and BABA will be equal. Suppose that modern humans and Neandertals diverged Y years ago, and that Vindija is V years old. Then, H1 (the living human) is separated from Vindija by 2*Y-V years of evolution, but H2 (the ancient human) is separated by 2*Y-V-X years. It is now expected that H2 will match Neandertal more often than H1 does at any site, and, consequently, there will be an excess of ABBA over BABA, and a non-zero statistic.
It will appear that ancient genomes may appear to be archaic-admixed even if they are not, and the older they are, the more archaic-admixed they will appear to be.
There is a different complication that may arise from the fact that the mutation rate per annum may not be the same in different human populations. If H1 and H2 are both modern humans, but the mutation rate per annum in the ancestry of H2 is less than the mutation rate per annum in the ancestry of H1, then H2 will be effectively closer to an archaic hominin (such as Vindija) than H1, and will appear to be archaic-admixed relative to H1.
It is not clear whether the mutation rate per annum has been the same in the ancestry of individuals who inhabit different climate zones, tend to have different body sizes, or have different generation lengths. Table S15 of Meyer et al. (2012) may suggest that it is not:
It appears that the the San- and Yoruba-specific branches are a a little longer compared to Eurasian-specific branches. This may contribute to a signal of archaic admixture in Eurasians.
In both described cases, it remains to be seen how much of the signal of admixture might be explainable on the basis of these effects, and how much will remain intact.