The K2 200m pairing of Heath and Schofield upgraded their bronze medal from London 2012 to silver at the World Championships in Germany behind Olympic champions Yury Postrigay and Alexander Dyachenko.
Rutherford meanwhile took bronze in the non-Olympic K1 5000m event and Ed McKeever failed to follow up his gold medal in the K1 200m at the London 2012 Olympics last summer as he finished sixth in the final in Duisburg.
And GB Canoeing performance director Anderson admitted it was too difficult to separate the performances of Heath and Schofield and Rutherford as Britain fell one medal short of equalling their performance at the 2011 worlds in Hungary.
"Medals haven't come easily to any nation this year and this was an outstanding medal for Liam and Jon," said Anderson. "I'm delighted for them both and they finished a lot closer to the Russians than they did in London last summer.
"Ed delivered a tactically good race in a high-class field. Germany's Max Hoff, who finished behind him in fourth place is an outstanding athlete with success in distance events so this was a great medal for Ed to win."
© Sportsbeat 2013