In theory it should not be possible for a non-owning player to modify the text labels.
Put this example in a script tool:
local list = world.get_label_list()
// list is now of type label_list_x
foreach(label in list) {
label.set_text("If I'm not the owner this shouldn't change :P.")
}
This is not allowed in network games, only for local games and is intended that way.