The fact that deaspiration in Greek took place after the change of Proto-Indo-European *bʰ, *dʰ, *gʰ to /pʰ, tʰ, kʰ/ (PIE *bʰn̥ǵʰús > παχύς (pakhús) not bakhús but Sanskrit बहु (bahú)) and the fact that all other Indo-European languages do not apply Grassmann's law both suggest that it was developed separately in Greek and Sanskrit (although quite possibly by areal influence spread across a then-contiguous Graeco-Aryan–speaking area) and so it was not inherited from Proto-Indo-European.
(For example, *ségʰō > *hekʰō > ἔχω /ékʰɔː/ "I have", with dissimilation of *h...kʰ, but the future tense *ségʰ-sō > ἕξω /hék-sɔː/ "I will have" was unaffected, as aspiration was lost before /s/.)
The evidence from other languages is not strictly negative: many branches, including Sanskrit's closest relative, Iranian, merge the Proto-Indo-European voiced aspirated and unaspirated stops and so it is not possible to tell if Grassmann's law ever operated in them.
In his initial formulation of the law, Grassmann briefly referred to aspiration throwback to explain the seemingly aberrant forms.
In the later course of Sanskrit, under the influence of the grammarians, aspiration throwback was applied to original mono-aspirate roots by analogy.
From a diachronic standpoint, the absence of these patterns in Greek is explained by the Proto-Indo-European constraint against roots of the form *T...Dʰ-.
Processes similar to Grassmann's law continue to work in Middle Indo-Aryan, although it tends to be inconsistent regarding direction, for example Sanskrit स्कन्ध (skandha) → khandha → Assamese কান্ধ (kandh), but भ्रष्ट (bhraṣṭa) → bhaṭṭha → ভাটা (bhata).
A similar effect takes place in Koti and other Makhuwa languages, where it was dubbed Katupha's law in Schadeberg (1999).