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They have proprietary rights to the data. (Longman Dictionary of Contemporary English)

He has no proprietary interest in the farm (=he does not own any part of it). (Longman Dictionary of Contemporary English)

This chapter discusses proprietary rights. These govern people’s ability to use and enjoy both land they physically possess and land physically possessed by others. Whilst technically all land is owned by the Crown, holding an estate in land, and in particular a freehold estate that gives one rights to possess, enjoy, and use the land forever, is tantamount to actual ownership. The other type of proprietary right is an interest in land. Whilst an estate gives one a slice of time to use and enjoy land one physically possesses, an interest gives the right to use and enjoy land physically possessed by another. Proprietary rights can be either legal or equitable in status. (Oxford Law Trove)

"Title" means ownership. But ownership can be "encumbered," for example, by a tenant with a lease, which is an "interest," something which is less than full ownership but which is legally enforceable and usually recorded if it has to do with real estate. "Interests" include those established in probated wills and in trusts, those established in mortgages and judgment liens, and those established in recorded easements. "Rights" is a hodge-podge term that applies to everything else. It can include contractor liens, homestead interests, prescriptive easements (common-law easements), the rights of neighbors under restrictive covenants, and many other things. (StackExchange)

These words, interest and right, are in no way similar. I can only suppose you are comparing “having interest in” to “having a right to.” A right to something presupposes ownership by inheritance or deed. To have an interest in a thing may mean some type of limited ownership, as in shares of stock or bonds, but interest can also mean a mere simple liking or taste for something. (Quora)

However, because the beneficiary has no proprietary interest in the trust fund, he cannot vindicate the property from the third party. (Nature and Constitution of Trusts - Scottish Law Commission)

Property law governs the various forms of ownership and tenancy in real property and personal property. It also provides the principles and rules by which disputes over property are to be resolved. (The Lawyer Portal)