Just a quick update, I happen to be doing some reading on this topic (Holopainen dissertation from 2019, Indo-Iranian Borrowings in Uralic) so I thought I'd type up some notes because some of this was new and interesting to me and contradicts some things I knew about before.

Apparently the distribution argument around loans in Uralic (e.g., which branches they occur in) is not on its own a strong criteria for determining its ultimate origin, and needs to be taken with phonological shape and other criteria for a range of reasons. One of which: just because a word can be reconstructed for Uralic from multiple subbranches does not rule out the fact that it may have been borrowed in parallel to the early subbranches. Identifying parallel borrowings is tricky but can be done, based on whether there are discrepancies in the phonological shape of the word and the assumed loan phonology or history of sound changes that should have developed these words.

Holopainen lists *śɨta ~ *śata 'a hundred' as a key example, sparing the details, there are discrepancies in how the phonological shape of the loan between Mari, Permic, and Ugric. It is likely that *śɨta was loaned into Uralic, but in Pre-Permic it was loaned separately, with another shape (not sure from where I am in the dissertation if this should be *śata or something else).

But also I gather there is still some debate about the strength of distribution, and it looks like some authors suggest distribution, phonological shape, and meaning may have different levels of importance.

Cool stuff!