I think they addressed this in the edit they made: >Correction: this post was edited on the 6 January to reflect the argument that if an n-clue grid is uniquel

I think they addressed this in the edit they made: >Correction: this post was edited on the 6 January to reflect the argument that if an n-clue grid is uniquely solvable then adding a digit to make an n+1-clue grid must also be uniquely solvable. So if there are no uniquely solvable 16-clue grids, there cannot be any grids with fewer clues that are uniquely solvable. Thanks to RealMurph and abooij.