Missing Demands

In Capernaum synagogue there's a stone with an engraving in the shape of the Star of David on it. Since this stone is in a Jewish environment researchers guess that it was a Jewish symbol. The fact is that nobody knows whether the community that used this synagogue ascribed to this shape the meaning that we ascribe to it today (sign of Judaism and/or Zionism and/or Israel) and nobody knows if the community that used this synagogue named it in the same name as we do.
Anyhow, there's quite a difference between the terms "symbol of Judaism" and "Jewish Symbol". Most of the papers I read so far bring a list of artifacts similar to the one found in Capernaum, artifacts that were found on different sites in ancient Israel. These have the shape of the Star of David but they don't have the matching name or meaning. We don't even know WHAT they symbolized.
IMHO a Star of David must meet all the above three demands (shape name and meaning) in order to differentiate it from other cultures' hexagram. Since all the artifacts found in ancient Israel have for certain only the shape of the symbol I don't consider them as more than hexagrams until the missing demands will be completed.