When bulk helium-4 is cooled below T = 2.18 K, it undergoes a phase transition to a superfluid, characterized by a complex wave function with a macroscopic phase and exhibits inviscid, quantized flow. The macroscopic phase coherence can be probed in a container filled with helium-4, by reducing one or more of its dimensions until they are smaller than the coherence length, the spatial distance over which order propagates. As this dimensional reduction occurs, enhanced thermal and quantum fluctuations push the transition to the superfluid state to lower temperatures. However, this trend can be countered via the proximity effect, where a bulk 3-dimensional (3d) superfluid is coupled to a low (2d) dimensional superfluid via a weak link producing superfluid correlations in the film at temperatures above the Kosterlitz-Thouless temperature. Recent experiments probing the coupling between 3d and 2d superfluid helium-4 have uncovered an anomalously large proximity effect, leading to an enhanced superfluid density that cannot be explained using the correlation length alone. In this work, we have determined the origin of this enhanced proximity effect via large scale quantum Monte Carlo simulations of helium-4 in a topologically non-trivial geometry that incorporates the important aspects of the experiments. We find that due to the bosonic symmetry of helium-4, identical particle permutations lead to correlations between contiguous spatial regions at a length scale greater than the coherence length. We show that quantum exchange plays a large role in explaining the anomalous experimental results while simultaneously showing how classical arguments fall short of this task.