I don't have any sources, this is based on conversations I've had with several of my Indian friends:
The Gita is both more monotheistic and more prescriptive than the Vedas. It is only after their contact with Islam that Hindus started feeling the need for their religion to be monotheistic and prescriptive.
This only got exasperated once the British came, as both the Muslims and the British gave them the impression that traditional polytheistic beliefs are somehow primitive compared to monotheistic religions.
It's also at that point (British colonization) that Indian culture started to unify, and a web of interrelated religious beliefs, whose only common factor was belief in the concept of Karma coalesced into a single religion called Hinduism.
That is probably the source of the counter opinion you mentioned: That the Gita gained more importance in Hinduism as Hindus tried to "Westernize" their religion.
P.S: In this context Islam is as much a Western religion as Christianity is.