In fact against most of his closest Soviet rivals he did not have that bad a score. The one notable exception was Mikhail Botvinnik who was +5 against him. A lot of this was down to the 1948 World Championship Tournament (where Botvinnik owned Keres), but the following game was a later example of Botvinnik's play against Keres.
Botvinnik,Mikhail Moisevich - Keres,Paul Petrovich [A29]
URS-chT Moscow, 1966