  Recently, there has been a growing interest in the relationships between
unrooted and rooted phylogenetic networks. In this context, a natural question
to ask is if an unrooted phylogenetic network U can be oriented as a rooted
phylogenetic network such that the latter satisfies certain structural
properties. In a recent preprint, Bulteau et al. claim that it is computational
hard to decide if U has a funneled (resp. funneled tree-child) orientation, for
when the internal vertices of U have degree at most 5. Unfortunately, the proof
of their funneled tree-child result appears to be incorrect. In this paper, we
present a corrected proof and show that hardness remains for other popular
classes of rooted phylogenetic networks such as funneled normal and funneled
reticulation-visible. Additionally, our results hold regardless of whether U is
rooted at an existing vertex or by subdividing an edge with the root.
