[blackbear_]

> would you happen to have the paper proving that somewhere?

Actually no I don't, but here's the intuition. Consider what happens in the limit when the bandwidth goes to zero: the kernel collapses to a delta function, i.e. K(x_i, x_j)=1 when i=j and 0 otherwise. The kernel matrix approaches the identity. The optimal coefficients solving the quadratic program approach zero. The SVM predicts zero almost everywhere except in a smaller and smaller surrounding of the training points, where the prediction equals the label of that point.