David Reich doubts the Denisovan origin of some HLA class-1 alleles, apparently because they have higher frequencies on the Asian mainland, while ( according to interviews) he has only found Denisovan ancestry among the peoples of island southeast Asia and Melanesia (and probably Australia). However, the amount of admixture required to pass an advantageous gene is very low.
Imagine that a given allele (an HLA allele in this case) has a 5% selective advantage. A single copy then has a 10% chance of reaching high frequency. So admixture of a single Denisovan individual could well be enough, which would probably correspond to an admixture level well under a tenth of a percent - too low for Reich to measure.
Or it might be the case that the first wave of anatomically modern humans entering east Asia admixed with Denisovans at the few-percent level, but that first wave was later displaced by a later wave (or waves) with low Denisovan admixture. Presumably the second wave would admix with the first at the few-percent level, which would almost erase the original Denisovan component. However, adaptive alleles don’t stay at their original low frequency. In that scenario, adaptive HLA alleles of Denisovan origin might have already been common in the first wave (~tens of percent) before the second wave hit.
No reason to assume Denisovans were the only Archaics in East Asia, or that they were even there for the arrival of the “second migration”. The phantom HLA alleles could very well be derived from an entirely different archaic “subspecies”, such as the descendants of the people represented by the Dali skull. Afterall, we didn’t even know about Denisovans 3 years ago, but we’ve known about archaic homo in China for a long time. All we need now is some DNA.