Partly true, but let's be clear about who is being indoctrinated about culture.

Khmer culture is basically an offshoot of the original Hindu, and then Buddhist culture from India. The language is the 'latin' of the region and based off sanskrit, and all the temples in the region are modeled on Hindu temples (representations of mount Meru).

Tai people came from SW China and colonized, if not assumed, this extant culture, and also of course intermingled and whatever.

So both populations share a deep and long history and are closely related.