Yes, those stars are important. While many images of her in he west do have them, they are not always found.
However I do not think they are absolutely universally found in byzantine images historically, though now today it is extraordinarily rare to not see them used.
Mother of God (The Virgin in prayer "orans position")
Pec Patriarchate, 14th century
So for the latin west (and maybe also some of the east) there are two possible explanations I can think of for why the stars would not be there.
#1 - though the stars are there at an early date in some regions, many of the oldest images which may have served as prototypes did not have the stars. Sometimes the reason western images (and liturgy) is more primitive is because it never developed far enough past it's paleo-christian (early christian) traditions. Perhaps that could be considered a conservative aspect of latinity.
#2 - sometimes in later repainting and touching up, important details may have been forgotten and or painted over.
Anyway, most images in the same book that this scan was in which are all italian from same period, do have the three star patterns.
So one can say this was also establishing itself as tradition in the west. However it is true that at some point that tradition was abandoned or perhaps "never fully established".
The primitive and or early christian quality of pre-14th c. latin paintings is sometimes not as harmonious with the sophisticated uniform and elaborate developments of the byzantine east during similar time period. By the time the west made more elaborate in painting, it had also become exclusively gothic/naturalistic in style. This makes the situation of sacred art for the latins somewhat inconsistent, confusing and complex. Though the 13th c. is a very impressive period in it's late romanesque art. Before it transformed into gothic the romanesque "went out with a bang" !
The Maestà from the Pushkin Museum of Moscow (la Maestà del Museo Puškin di Mosca) (painted in florence by italians, but bought by a russian art collector in the early 20th c.) (It has a western version of the assumption on it , which is interesting.)
another one without any, from the west: (one of my favourites.)
Master of the Bigallo Crucifix (Italian, fl.1225-1255)