Agreed, but They have started taking the Ownership, that's what the problem is. They want to sail on two boats. Both Islam and Vedic civilization, to show them superior.
Ideas aren't anyone's to own for themselves. Here's a quote from my favorite US president, Thomas Jefferson:
"If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me. That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density in any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement or exclusive appropriation. "
So don't worry about what these Pakis are claiming, just be confident in your own identity. Indian Civilization (of which Vedic is a part) has always allowed for many ideas & philosophies to develop, grow and flourish. This is similar to Hellenic Civilization and in stark contrast with monotheistic theocracies (Europe during the dark ages, Islamic world to this day). Europe came out of the dark ages when they rediscovered their pre-Christian roots, and began reading the works of Socrates, Epicurus, Marcus Aurelius & other Greco-Roman philosophers. Out of this came the renaissance and enlightenment, because they realized in the words of Shakespeare:
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.
- Hamlet (1.5.167-8), Hamlet to Horatio
So if claiming the Vedas as their own helps them come to this realization, then what's the harm?