[murky]

In 1926 we went undefeated and tied Alabama (!)  in the 1927 Rose Bowl.  We were undefeated and rated #2 in 1940.  #4 in 2010 and #3 in 2015.  We probably have the most H award runner-ups in at least the last 20 years.  

Here's the number of runners-up by college.  Turns out you're correct (this is since the inception of the award, not the last 20 years):

6  Stanford

5  Oklahoma

4  Iowa, Notre Dame, Southern California, Tennessee

3  Army, Ohio State, Penn State, Pittsburgh, Purdue, 

2  Alabama, Arkansas, Georgia, Georgia Tech, Michigan, Minnesota, Nebraska, North Carolina, Texas, Tulsa

1  BYU, California, Clemson, Colorado, Columbia, Cornell, Florida, Florida State, Indiana, Iowa State, Kansas State, LSU, Maryland, Oklahoma State, Pennsylvania, San Diego State, SMU, Syracuse, TCU, Temple, Texas A&M, Wisconsin

Other distinctions likely never to be matched are having the runner up 3 years in a row, and the same player as runner up twice.

[murky]

In 1926 we went undefeated and tied Alabama (!)  in the 1927 Rose Bowl.  We were undefeated and rated #2 in 1940.  #4 in 2010 and #3 in 2015.  We probably have the most H award runner-ups in at least the last 20 years.  

Here's the number of runners-up by college.  Turns out you're correct (this is since the inception of the award, not the last 20 years):

6  Stanford

5  Oklahoma

4  Iowa, Notre Dame, Southern California, Tennessee

3  Army, Ohio State, Penn State, Pittsburgh, Purdue, 

2  Alabama, Arkansas, Georgia, Georgia Tech, Michigan, Minnesota, Nebraska, North Carolina, Texas, Tulsa

1  BYU, California, Clemson, Colorado, Columbia, Cornell, Florida, Florida State, Indiana, Iowa State, Kansas State, LSU, Maryland, Oklahoma State, Pennsylvania, San Diego State, SMU, Syracuse, TCU, Temple, Texas A&M, Wisconsin

Other distinctions likely never to be matched are having the runner up 3 years in a row, and the same player as runner up twice.