From a 1994 review of E.coli single-stranded binding protein (SSBP) in Annual Reviews of Biochemistry, it would appear that at least 35 nucleotides (nt) of single-stranded DNA are required for binding of SSBP to occur.
From a paper in Trends in Analytical Chemistry describing recombinase polymerase amplification I read that the first step in the procedure (A, below) is to add the primers to the recombinase, forming a complex between the two, and that it is only at a subsequent stage (D) that SSBP is added.
As the length of primers normally used is also apparently ca. 35 nt, I presume that the length of primer available to the SSBP is less than 35 nt, and it is for this reason that SSBP is unable to bind to it. (In the cartoon there would appear to be no primer available, except, presumably, for the DNA.)
An alternative would be that the recombinase hinders the binding of the SSBP.