My understanding is that “banana oil” (which smells powerfully of bananas – I’ve smelled it) actually has nothing to do with bananas (unlike other esters, like wintergreen oil, which do). It’s Isoamyl Acetate. But the relevant Wiki page doesn’t confirm or deny the banana connectionL:
On thinking about this more, I suspect that you’re both probably right that what we used was synthetic, but that a banana’s smell probably is because the banana produces isoamyl acetate naturally.
I used to brew a hefe weissen (wheat beer) that had a slight banana scent caused by the yeast strain producing isoamyl acetate.