If, as in this paper, we allow ourselves to set the kernel after seeing the data, then the statement in the title is trivial: if my learning algorithm outputs function f, I can take the kernel K(x,x')=f(x)*f(x').
The result is interesting insofar as the path kernel is interesting, which requires some more thought.
The result is interesting insofar as the path kernel is interesting, which requires some more thought.