Of course it is a stretch, and I never inferred otherwise, did I.
But what complicates the vagueness of your prior answers just a tiny bit is that many historians think there were no viable Phoenicians left by the time a small number of Southern Kingdom Israelites began to be called Jews (~500 BC). The Phoenicians reached the peak of their culture around l,000 BC, the same time David's Kingdom of Israel reached it's short zenith.
Of course there were no Jews during Davids time, only Israelites, and they had not yet even split into Northern and Southern Kingdoms.
For example, if Jesus was a Jew, why did he have a Puerto Rican name?