... So the original question appears to hinge on having a referee or someone declaring the frozen ball as "frozen"
Yes. The OP didn't specify whether the frozen call had been made before the shot.
If there is no referee, the seated player will normally call the ball frozen and if the shooter objects they can inspect the ball together. Some shooters will call the ball frozen on their own (a frozen ball is to the shooter's disadvantage).
The rules did not have an explicit "player must be notified of a frozen ball" clause until 1977 and it was worded unclearly when it did appear.