[R-meta] Unrealistic confidence limits for heterogeneity?

<Nerdy follow-up question>

One can of course construct a dataset where the likelihood profile peaks

essentially at -min(vi) (or rather, just a smidge above it), which might
suggest that a value of tau^2 that is even smaller than -min(vi) could lead
to an even larger likelihood, but then one would have to allow negative
weights.

Wolfgang, do you know for sure that this is the case? I was under the
impression that the profile likelihood in tau^2 (and the REML likelihood)
should always have a maximum in the interior of (-min(vi), +infinity). I
haven't worked through a full derivation, so was just curious whether you
might know to the contrary.