So too, more briefly, Hesychius s.v.
This infinitive occurs in Aristophanes, Wasps 1241 (web address 1), where it is presented as an already-existing song or proverb. Zenobius (1.70) and other paroemiographers present both proverb and gloss more fully: "to play the fox to another fox: in reference to those attempting to deceive their own kind".
For other proverbs involving foxes cf. alpha 1391, alpha 1392.