Thanks for your feedback: this is all a bit of a tricky area. Just to be 100% clear, let's define some terms:
RHEIGHT = "Height" as measured in the RAINFOR protocols, which is really stemlength because that is what is most relevant for biomass estimation.
VHEIGHT = Vertical height to crown top, which for a leaning tree will be less than RHEIGHT. Chave's papers talk about "total tree height" so his H is technically VHEIGHT (and for Larjavaara and Muller-Landau too).
AGLB = AboveGround Live Biomass INCLUDING both stem and branches.
In most papers this is the same as AGB ("AboveGround Biomass", e.g. Chave et al. 2005) but I think it's clearer to say "live" to remind us that coarse woody debris and leaf litter are excluded from this (Chave's paper never mentions litter or CWD but because he talks about the AGB "of a tree" we know litter and CWD were excluded). It's debatable whether live canopy leaves were included in Chave's AGB, but let's assume that they were (the leaves are a negliible component of AGLB anyway so this doesn't matter too much).
OK: so the Chave et al. (2005) paper talked about estimating AGLB from diameter data and VHEIGHT. Because we know that Chave worked almost entirely in lowland forests with only a very small number of leaning trees, it's fair to assume that his VHEIGHT was approximately the same as his RHEIGHT in those study forests.
In a cloud forest context where there are many leaning trees, it's better to use those Chave allometries and substitute H=RHEIGHT not H=VHEIGHT because otherwise AGLB is going to be underestimated.
Does all that make sense?
PS. Chave et al. (2005) is the Oecologia paper of Jerome Chave that is available online for free at http://www.winrock.org/ecosystems/files/Chave_et_al-2005.pdf