Consider a pair of transient random walks where the law of the second path is Gibbs transformed with a Hamiltonian proportional to the number of collisions with the first. The fact that here, the quenched and annealed critical points differ can be proved via a conditional LDP or via coarse-graining and fractional moment estimates. We discuss this result and its implications for the study of intermediate phases in certain interacting stochastic systems, in particular directed polymers in random environment and branching random walks in space-time random environment.