Assuming that fangraphs' stats for homeruns and RBI since 1920 are accurate, then for hitters with at least 300 PA since 1920:
-For players with 30 or more homeruns, Curtis Granderson's 2016 of 30 homers and 59 RBI is indeed the lowest (RBI - HR = 29)
-For players with 20 or more homeruns, the lowest RBI-HR total belongs to Chris Hoiles of the 1992 Baltimore Orioles, who had 20 dingers and only 40 RBI (RBI - HR = 20)
-For players with 10 or more homeruns, the honour belongs to Scott Hairston of the 2008 Padres, who hit 17 homeruns to go along with 31 RBI (RBI-HR = 14)
-For 5 homeruns or more, Karl Rhodes of the 1994 Cubs has the record, hitting 8 homeruns and driving in 19 (RBI-HR = 11)
-For at least 40 homeruns, Barry Bonds' 2003 campaign has that record, he hit 45 homeruns and drove in 90 (RBI-HR = 45)
-Lastly, for at least 50 homeruns, this one came during Willie Mays' only 50+ homer season, where he hit a modest 52 cuadrangulares and helped his teammates score 112 runs (RBI-HR = 60)
Trust me, I checked.