Neither Playford nor Praetorius claim to have composed the tunes associated with them. Praetorius collected a lot of his music themes, as did many other composers - the Terpsichore, in which Parson's Farewell and at least one other 'Playford' tune, "The Merry Wassail" occur, is described on the title page as "containing all sorts of French dances and songs", so clearly not intended to be original work. Musicians travelled all over Europe, mostly looking for cheap beer, and it's quite likely that the same tunes were used by Playford's sources and by the French dance masters from whom Praetorius collected. Recognisable versions of "Parson's Farewell" also occur in early seventeenth century Dutch collections.
Praetorius's patron, Duke Heinrich Julius, was closely related to both Danish and English Royalty, and English musicians performed at the court. So the tune was called "La Bouree" when praetorius collected it, and "Parson's Farewell" when Playford picked it up - neither is invalidated by the other. And yes, it is interesting. Thank you for sharing this.