There's no inherent right to anything, really. The statements in whatever declaration or philosophy are just arbitrary lines. Physical property rights are just as arbitrary as the divine right if kings (and incredibly closely related when that property is inherited!)

The argument really isn't based on rights, it's based on the rules of the game have been that people that make things get to decide what folks get to do with those things via licensing agreements, except for a very small set of carve outs that everyone knew about when they made the thing. The argument is consent. The counter argument is one/all of ai training falls under one of those carve outs, and/or it's undefined so it should default to whatever anyone wants, and/or we should pass laws that change the rules. Most of these are just as logical as if someone invented resurrection tomorrow, then murder would no longer be a crime.