No you absolutely weren't right, you tried to correct my statement (paraphrasing) of 'We know Nero wasn't fiddling' with 'Actually we know Nero wasn't fiddling because fiddles weren't invented'. You literally proved my statement while trying to say I was wrong.
Not to mention, the link you provided indeed states that evidence points to their existence in 3000 BC - in ancient Mesopotamia. Their earliest known existence. From which spread to Egypt and Greece, specifically Greece in the form of the pandura. The only thing I'm technically wrong about here is assuming ancient Greece isn't a part of Europe, because the Greeks themselves didn't identify as European. They actually invented the term.
You need to actually read. I'm not interested in continuing to give you history lessons.