I've read that path comes from Old English pæþ from Proto-Germanic paþaz. The word is supposedly a cognate with Greek pátos as well as other Indo-European words beginning with the voiceless stop, and not the voiced stop. Doesn't Grimm's Law mean that voiceless stops become voiceless fricatives and voiced stops become voiceless? Cause it seems as though this is neither.
The Wiktionary entry for "path" does a terrible job of making this clear, but the reconstructed Germanic form *paþaz is generally thought to be a loanword taken from some other Indo-European language, not a word inherited within Germanic from PIE. In this case, "path" would be indirectly related to "πάτος", but they wouldn't constitute a cognate set for the purposes of historical linguistics.
This is mentioned on the separate Wiktionary entry for *paþaz itself, which suggests it was borrowed into Germanic from an Iranian language. I don't know what the consensus is among professional etymologists, but I don't think any of them would accept an etymology where "path" is supposed to have developed completely within Germanic from a PIE root starting with "p", because there is no known mechanism that would explain such an exception to Grimm's Law. (Sometimes unexplainable exceptions to sound changes do occur, such as English "broad" being pronounced as /brɔːd/ rather than /broʊd/, but accepting these generally requires a large amount of additional evidence about the evolution of a word.)
I found a Language Hat blog post with comments that mention the etymology of this word: Paths.
Grimm's Law is a process that was active at some point in the history of Germanic. It didn't stay active forever (as indicated by the fact that modern English speakers don't change /p/ in loanwords to /f/). So if a loanword with /p/ was borrowed into Germanic before Grimm's Law applied, we'd expect to see the reflex of Proto-Germanic /f/ in modern Germanic languages. But if a loanword with /p/ was borrowed into Germanic after Grimm's Law had already run to completion, we'd expect to see the reflex of Proto-Germanic /p/ in modern Germanic languages.
So loans are unaffected by Grimm's Law? I didn't know that. Nov 12, 2016 at 21:12
1@ScottClendenin - And, conversely, we can use the shift or lack thereof to date the borrowings (for instance, we know that "beef" was borrowed into English before the Great Vowel Shift, exactly because it is pronounced /bi:f/; oeuvre was borrowed after the GVS, since it is pronounced /'əːvɹə/). Or, the other way round, Kaiser was borrowed into Germanic from Latin before phonetic changes in Latin turned its pronounciation into /'sɛ.zar/. Nov 14, 2016 at 13:12
From memory (from reading some book in the past - i'm not that old) I believe it was borrowed from Scythian after Grimm's law had happened and that it was the Scythian word for their royal roads.
The Online Etymology Dictionary cites authors that believe it is not a cognate with Greek pathos, but a borrowing from Iranian, probably via Scythian. But they seem skeptic of this, and say that the initial /p/ is "a puzzle".