Couple points.
This theory is almost universally held by historians and other scientists outside India. In India it is considered by many to be politically incorrect. Their notion is that the Aryans originated in India and spread north and west from there.
Some Indians get remarkably angry when their ideas on this point are challenged. Psychologically I think this is based on the, to me, very odd notion that the commonly accepted theory is trying to say Aryan Indian society is really European or "white" in origin, and therefore somehow to denigrate Indian society.
The "color" of Indians is more related to geography than caste. While I'm sure the "white" upper caste and dark lower cast idea has some relationship to reality in some areas, in much of southern India, for instance, the upper castes are just as dark as the lower ones.
The Indian word for caste, varna, actually means "color," BTW.
Yes, some Indians in recent years have been trying to invent a more psychologically satisfying history, but that is true of many people. It is nothing more than the Indian version of “black studies”.
While there is certainly a geographical aspect to skin color in India, the lower castes certainly tend to be darker. The geographic aspect to skin color is also a reflection of the invasion. The “India” that was invaded did not have the geographic boundaries of the “India” of the British Raj or the boundaries of the independent “India” created by the British. The culture of Aryan “India”, of course, spread beyond Aryan “India”.
Major subsequent cultural influences were the Moguls and the British. Interestingly, all three major influences are caucasian peoples, and many Indians and Pakistanis are Caucasian.
Linguistically, the evidence is quite clear. Moreover, the Aryan tribes moved in other directions as well. The modern language that most directly reflects “Indo-European” of the Aryan tribes is Lithuanian. Lithuanian, by the way, shares many basic words with Sanscrit - e.g. the words for horse, wagon, and fire are identical with Sanscrit).