> OTOH, absolute pitch means that learning a fiddle tune by ear takes only a couple of choruses

That doesn't require perfect pitch. Most of the YouTube musicians noted for making videos of going on sites like Omegle and its successors and taking requests which they the then play perfectly after a short listen to the original if they don't know the song do not have perfect pitch for instance. Examples include The Dooo (guitar and piano), Frank Tedesco (piano), and Rob Scallon (violin).