The supposed basis is detailed in this thread:
In 1913, the United Daughters of the Confederacy presented the Silent Sam statue to the University of North Carolina. In a speech marking that presentation, a UDC official expressed the wish that it should “stand forever as a perpetual memorial”.
The UDC says this was a condition of the gift, any breach of which would cause ownership of the statue to revert to the UDC. It holds that such a breach occurred in January 2019, when the university removed the statue from its plinth.
The UDC subsequently transferred its purported rights in the statue to the Sons of Confederate Veterans.
Mr Muller calls bullshit on the above, mostly because gift conditions of that sort typically have to be made crystal-clear in writing, rather than in a throwaway comment in a speech; but also because it seems the sculptor who created the statue was contracted directly by the university, not the UDC.