  We use publicly available data for the Millennium Simulation to explore the
implications of the recent detection of assembly bias and splashback signatures
in a large sample of galaxy clusters. These were identified in the SDSS/DR8
photometric data by the redMaPPer algorithm and split into high- and
low-concentration subsamples based on the projected positions of cluster
members. We use simplified versions of these procedures to build cluster
samples of similar size from the simulation data. These match the observed
samples quite well and show similar assembly bias and splashback signals.
Previous theoretical work has found the logarithmic slope of halo density
profiles to have a well-defined minimum whose depth decreases and whose radius
increases with halo concentration. Projected profiles for the observed and
simulated cluster samples show trends with concentration which are opposite to
these predictions. In addition, for high-concentration clusters the minimum
slope occurs at significantly smaller radius than predicted. We show that these
discrepancies all reflect confusion between splashback features and features
imposed on the profiles by the cluster identification and concentration
estimation procedures. The strong apparent assembly bias is not reflected in
the three-dimensional distribution of matter around clusters. Rather it is a
consequence of the preferential contamination of low-concentration clusters by
foreground or background groups.
