Thanks for the help so far. The thing that gets me is that the same product purchase works fine when done by a logged in user. I even tried making a purchase as an anonymous user, then logging in with the created account and making a purchase of the exact same product and it'd work the second time. So I think that rules out a few things.

There is no "User can now download..."

Anonymous users should be able to purchase file download products though, correct? It should be associated with the account that's created for them during the checkout.

The order shows as completed, the same order status which works when done by an authenticated user.