  The Message-Passing Approach (MPA) is the state-of-the-art technique to
obtain quasi-analytical predictions for percolation on real complex networks.
Besides being intuitive and straightforward, it has the advantage of being
mathematically principled: it is exact on trees, while yielding generally good
predictions on networks containing cycles as do most real complex networks.
Here we show that the MPA does not perform its calculations on some ill-defined
tree-like approximation of the network, as its formulation leads to believe,
but rather considers a random network ensemble in which the original network is
cloned and shuffled an infinite number of times. We conclude that the fact that
the MPA is exact on trees does not imply that it is nearly exact on tree-like
networks. In fact we find that the closer a non-tree network is to a tree, the
worse the MPA accuracy becomes.
