Addendum: in Eklund's paper's supplementary PDF, the following can be found:

«Supplementary Figure 14 shows that the SACFs are far from a squared exponential. The empirical SACFs are close to a squared
exponential for small distances, but the autocorrelation is higher than expected for large distances. This could be the reason
why the parametric methods work rather well for a high cluster defining threshold (p = 0.001), and not at all for a low threshold
(p = 0.01). A low threshold gives large clusters with a large radius, for which the tail of the SACF is quite important. For a high
threshold, resulting in rather small clusters with a small radius, the tail is not as important.»

This seems to go along the same lines as what we discussed before, so I would say it's likely that CONN's denoising reduces the extent of this issue :-)