The bolded part reminds me of what I wrote in my review of Atzmon et al. regarding the choice of parental populations and how they affect admixture estimates. The "Middle Eastern" component estimate will increase if central and eastern Europeans are used as representative of the European admixture, while the "European" estimate will increase if Italians are used. But, the same applies to the other end of the continuum: if ancestral Jews were indeed like current Middle Easterners such as the Druze or Palestinians, but the latter may have moved (in genetic space) away from ancient Levantines due to subsequent admixture (Arabs, and in the case of Palestinians even Africans): this would reduce the inferred Middle Eastern component.
Estimating admixture percentages in the absence of clear knowledge about parental populations is no easy thing, but the intermediate-leaning-on-Europe status of AJ relative to living Europeans and living Middle Easterners seems to be a pretty secure conclusion.