Is the Jacobian space a global workspace?

In "Verbalizable Representations form a Global Workspace in Language Models", Gurnee et al define a special component of the activation space in a language model: the Jacobian space, or J-space for short. Representations in the J-space are verbalizable in that they are especially likely to influence the words used in the language model's outputs. Gurnee et al argue that the J-space functions as a mechanism for conscious access (or access consciousness). They also argue that it closely resembles a well-known proposed mechanism for conscious access: the global workspace. I argue that while the J-space is interesting and powerful, its connections to the global workspace and to access consciousness have been somewhat overstated.