
Obviously, I can’t speak to the details of linguistics and area studies history. But I can say a bit about genetics because over the years I’ve assembled a reasonable data set of Asians, both public and private. The 1000 Genomes collected Vietnamese from Ho Chi Minh City in the south. I compared them to a variety of populations using ADMIXTURE with 5 populations.

You can click to enlarge, but I can tell you that the Vietnamese samples vary less than the Cambodian ones, and resemble Dai more than the other populations. The Dai were sampled from southern Yunnan, in China, and historically were much more common in southern China, before their assimilation into the Han (as well as the migration of others to Southeast Asia).
Curiously, I have four non-Chinese samples from Thailand, and they look to be more like the Cambodians. This aligns well with historical and other genetic evidence the Thai identity emerged from the assimilation of Tai migrants into the Austro-Asiatic (Mon and Khmer) substrate.
Aside from a few Vietnamese who seem Chinese, or a few who are likely Khmer or of related peoples, the Vietnamese do seem to have some Khmer ancestry. Or something like that.

The lower Mekong region is a fascinating zone from the perspective of human geography and ethnography. Divided between Cambodia and Vietnam, until the past few centuries it was, in fact, part of the broader Khmer world, and historically part of successive Cambodian polities. Vietnam, as we know it, emerged in the Red River valley far to the north 1,000 years ago as an independent, usually subordinate, state distinct from Imperial China. Heavily Sinicized culturally, the Vietnamese nevertheless retained their ethnic identity.