Upon further investigation, there seems to be a problem when editing a product that already has non-shippable file downloads attached to it. Here is what I have found:

Test #1
1) Edit product that already has file downloads attached, and those file downloads are set to be non-shippable.
2) Select the "Product and its derivatives are shippable." checkbox on the product edit page, and Submit the form.
3) Form is re-displayed with the checkbox checked.
4) Navigate to view the product page, then return to the product edit page.
5) "Product and its derivatives are shippable." checkbox is unselected.

Test #2
1) Edit product that does not already have file downloads attached.
2) Select the "Product and its derivatives are shippable." checkbox on the product edit page, and Submit the form.
3) Navigate to the "Features" tab for the product, add file downloads, and set them to be non-shippable.
4) Navigate to view the product page, then return to the product edit page.
5) "Product and its derivatives are shippable." checkbox is selected, and shipping is shown properly on the shopping cart.

Seems to be that Test #1 overrides the checkbox.