FYI I researched this a bit. Most coffee is hand-picked, with Brazil (featured in the video), being the exception.
Brazil is generally known for mass production low quality coffee grown at a lower altitude, which might be what you find in a can like grandparent said, but is less popular in the more premium scenes.
The cost of raw coffee has nearly tripled in 18 months, that's what's driven the price increases. That has not been due to the cost of processing and shipping so much as poor coffee growing seasons in major growing areas reducing primary production. Though growing, processing, and transport inputs have all suffered a lot of inflation in the past 5 years too, to be sure.