Also based on Suetonius' text!
Well, yes, but this isn't my fault, but the fault of the translations. The Latin original is more ambigous
et senatus in asserenda libertate adeo consensit, ut consules primo non in curiam, quia Iulia vocabatur, sed in Capitolium convocarent, quidam vero sententiae loco abolendam Caesarum memoriam ac diruenda templa censuerint.
Libertas is not the thing same as res publica (libera) ... You're right.