PIE *bhag- and Armenian bak

This is a follow-up on my thoughts on PIE *b^hag. I’ve come across an article by Hrach Martirosyan (“The place of Armenian in the Indo-European Language family: the relationship with Greek and Indo-Iranian”, Journal of Language Relationship, No. 10 / August 2013, p. 85 - 138), PDF here, where he adduces Armenian bak “courtyard; sheep pen, sun or moon halo” (missing in NIL) as a cognate of Indo-Iranian *b^ha:gá-: Sanskrit bha:gá- m. “prosperity, good fortune, property, personified distribution”, Old Avestan ba:ga- “part”, the descendants of which took on the meaning “landed property, fief, garden” (p.99, §5.1.3). Martirosyan admits the possibility that this is not a cognate, but an old loan from Iranian; he names one argument for it being a loan, namely the fact that the Armenian word is an a-stem, while the Indo-Iranian correspondences are o-stems; incorporation as an a-stem seems to be the expected outcome for an Iranian *ba:ga-; as another argument for a loan I would also see the fact that there seem to be no other formations from a root *b^hag- in Armenian. On the other hand, it would have to be an old loan from before the Armenian consonant shift, but Martirosyan admits that there are other such loans.

If this is not a loan, but a cognate, it would require a proto-form *ba:g-a:-, which could be explained as a Vrddhi-formation from *b^hag- or point to a PIE *b^heH₂g-eH₂- (Martirosyan’s reconstruction). Therefore, accepting bak as a cognate would in any case require us to posit a root PIE *b^hag- or b^heH₂g- separate from *b^heg- “break” (continuants of the latter root are well-attested in Armenian).