We show that estimating the probability of collective absence is highly nontrivial once both social interactions and latent external forcing are present. While observing a proxy variable related to the latent forcing substantially improves inference, practical identifiability remains weak in finite samples. Numerical experiments reveal a rugged likelihood landscape with multiple competing minima and approximate compensation directions between latent forcing and social coupling strength. In particular, different parameter combinations may yield very similar likelihood values while implying substantially different estimates of the latent forcing probability. Extensive optimisation experiments demonstrate that the resulting ambiguity is strongly sample-dependent and persists even for moderately large sample sizes. Nevertheless, sufficiently informative proxy observations substantially improve estimation accuracy. Our results highlight the distinction between structural identifiability in principle and practical identifiability in finite samples for latent-variable network models.