That's simply not even remotely close to being true.
But onto your request for run producers.
45 guys had 80 or more rbi in 2013.
Less than two per team in baseball.
Here's the list of guys that drove in 80 runs or more that are not home run hitters:
Yadier Molina
Kendry's Morales
Ian Desmond
Anthony Rizzo
Alex Rios
Alex Gordon
Billy Butler
Martin Prado
Jonathan Lucroy
Victor Martinez
Torri Hunter
Carlos Beltran
Michael Cuddyer
Andrew McCutchen
Jason Kipnis
Marlon Byrd
Mike Napoli
Matt Holiday
Adrian Gonzlez
Brandon Phillips
Freddie Freeman
There are three special players in no particular order that have good power and great speed:
Mike Trout, Hunter Pence, Robinson Cano
So out of the 45 guys last year that had 80+ rbi we see that more than half are not power hitters.
What's the point? You need run producers, not home run hitters. You need guys that can get on base and guys that can hit when runners are on base.