An interesting question! I suspect that the answer lies in the fact that the Public Bodies legislation applies to all tiers of local government and countless other public bodies, whereas the LGA reference is specific to parish and town councils. Higher authorities have emergency powers that are not necessary in local councils, so there is no legitimate reason to call a meeting at shorter notice. There is a shorter notice provision in the model standing orders for committees of local councils, but this relates to the provisions elsewhere in the model for councils to determine public access and notice requirements for their committees.