I'm glad he got paid. It was done in bad faith (much like the ScarJo case). He does allow for covers — Rod Stewart's Downtown Train cover paid for his swimming pool.
In the US, artists don't get to 'allow' for covers or not. The words and composition of a song are covered under a mechanical license. The recording and performance is covered under a different license. Under U.S. law, the mechanical license is a compulsory license - the rightsholder must give a license to anyone who applies and pays for it. The payment is standardized and includes royalties, so it's a pretty good deal for anyone who writes a song that gets a popular cover.
The Blind Boys of Alabama do great covers of Jesus Gonna Be Here and Way Down in the Hole, both on the Spirit of the Century album. The version of Amazing Grace set to the music of House of the Rising Sun, though, is to me the standout on an excellent album.