  In [1] we pointed out that in the Dark Dimension scenario [2] theoretical
issues arise when the prediction for the vacuum energy $\rho$, that is obtained
from swampland conjectures in string theory, is confronted with the
corresponding result for $\rho$ in the field theory limit. One of the problems
arises from the field theory side and is due to previous results for $\rho$
that, according to our analysis, turn out to be incorrect, although widely
spread. Our work was challenged in [3]. Here we show why in our opinion the
claims in [3] are inconsistent, actually based on arguments deprived of
physical meaning, providing further support to our findings. We conclude by
discussing ideas on the physical mechanism that could trigger the suppression
of large UV contributions to $\rho$.
