Tracking closely spaced targets: Bayes outperformed by an approximation?

In theory, a good joint particle filter allows to approximate the exact Bayesian filter solution arbitrarily well. This has motivated a strong and successful development of single target tracking particle filters. Nevertheless, for tracking multiple closely spaced maneuvering targets, there is evidence in literature which seems to contradict the theoretical expectation. The mystery of this apparent contradiction is analysed in this paper. For true Bayesians, only one outcome would be acceptable: a proper analysis should result into a logical explanation which can be used to the advantage of both Bayesian and particle filtering approaches towards tracking multiple close maneuvering targets.