  We show that if the flat-spacetime wavefunction in the spin network basis of
Loop Quantum Gravity has a large-spin asymptotics given by Rovelli's ansatz
then the corresponding graviton propagator has the correct large-distance
asymptotics nonperturbatively and independently of the spin foam model used to
describe the evolution operator. We also argue that even in the Rovelli
approach the wavefunction should satisfy the Hamiltonian constraint and we give
an explanation for the spin parameter appearing in Rovelli's ansatz.
