I changed Billing address to be skipped in checkout, but it isn't

I've gone to:
E-COMMERCE CONFIGURATION > CUSTOMER > GLOBAL SETTINGS
and set "Billing address" to "Only with shippable."

I've then created a product type "Audio file download" and gave it a "file download feature." Then in my product content type "Downloadable song" I've selected the "Audio file download" as the associated product type.

But when I click "Add to cart" and then "Checkout" I'm presented with "Billing address" form (along with "Payment details" and "Order summary").

The same thing happens if I associate my content type with "Generic product".

I've done a little bit of debugging, and as far as I can tell, the function ec_checkout_get_screens in ec_checkout (line 319) should be called at some stage in the checkout, except it isn't.