GNG increases when in ketosis, but is still capped because ketones regulate the GNG process. That is the effect which was observed here. It says it right there in the synopsis:
"Glucose concentration was lower (4·09 (sem 0·10) v. 4·89 (sem 0·06) mmol/l, P < 0·001) and β-hydroxybutyrate concentration was higher (1349 (sem 139) v. 234 (sem 25) μmol/l, P < 0·001) after the high-protein compared with the normal-protein diet."
β-hydroxybutyrate is a ketone body.
Note that this contradicts your statements that GNG will kick you out of ketosis. It absolutely will not.
To repeat: GNG is constant, regulated by ketones, and its relative level is not driven by protein demand, but by glucose depletion.
"Glucose concentration was lower (4·09 (sem 0·10) v. 4·89 (sem 0·06) mmol/l, P < 0·001) and β-hydroxybutyrate concentration was higher (1349 (sem 139) v. 234 (sem 25) μmol/l, P < 0·001) after the high-protein compared with the normal-protein diet."
β-hydroxybutyrate is a ketone body.
Note that this contradicts your statements that GNG will kick you out of ketosis. It absolutely will not.
To repeat: GNG is constant, regulated by ketones, and its relative level is not driven by protein demand, but by glucose depletion.