I would not say that. The simple answer is that they were basically herders and did not know any script, so transferred their lore orally. When the initial migration took place, the indigenous people liked Sanskrit and adopted it, speaking it as best as they could do and mixing it with their own words. Later the Pundits/scholars arrived with Vedic Sanskrit. Sure, they were very particular about pronunciation. Panini attempted to harmonize/standardize the Vedic Sanskrit and Prakrit, and I should say succeeded nicely, and came up with modern Sanskrit. Later, the scholarly use of Prakrits declined and Jains and Buddhists too wrote and discoursed in Sanskrit.