This urn is date to the 3rd c. BCE, so it's not very significant in saying what the original myth was. The Etruscan did already use the symbol of Medusa's head as having the power to heal and kill as early as the 6th c. BCE, appearing on temples and such. The gorgon as a protector is also found before that in Greece, the earliest mention of her is in Homer (then the Theogony and Hesiod in the same period) where she was already a fierce guardian of the underworld and nothing else, so in that period, the Greeks and Etruscans had similar views.

The evolution that we know better developed in the Perseus myth through the 6th and 5th c. BCE, which is later than her early Greek appearances but fairly soon after the Etruscan use of her. And it's only as late as the Roman poet Ovid that we get Athena punishing Medusa into a hero-killing monster. Perseus also has influences from Babylonian Marduk and Tiamat, with one 6th c. BCE Corinthian vase where he throws rocks at Cetos with Andromeda behind him - it's almost a straight copy of a common depiction of Marduk killing Tiamat, except the rocks were stars. I'm not sure if we know where the Medusa-killing myth was inspired from, but the "old witch controling seasons and healing and killing and turning people to stone" also exists across European and Celtic folklore, we just don't know how old those are. It may just be a case that the Gorgon represented fear of the unknown beyond the limits of the mortal world, and Perseus was simply a myth that represented mankind overcoming that fear, more than the usual Greek propaganda. Considering that the Greeks were also using her as that symbol, on maps and graveyards and such. Perseus just seems to be a mishmash of various unrelated heroic deeds that the Greeks tossed in a blender. Explaining her head on the aegis with a myth came later.

But yeah, agree on Greece generally transforming foreign symbols into monsters that the Greek gods punished for their hero to kill.