Hmm, Box.net will probably work. What we will is a direct, static link to any file you are storing on Box.net that we can access remotely.
Box.net's features say they provide web links to your files, but some file sharing sites like Mediafire or actually give you an URL with a random string that redirects to your file rather than the actual URL (similar to how we provide downloads to your buyers, they do not get access to the actual location of the file) -- that won't work for our purposes because we won't be able to access the file directly.
I've not spoken to any users who have worked with Box.net so I can't make a solid recommendation, but we can guarantee that Amazon S3's storage service will work, and they even have a free usage tier that can give you up to 5 GB of storage with enough bandwidth to meet remote hosting needs: http://aws.amazon.com/free/
On our end you would need at least an $18/mo subscription. That is the least expensive option for an account with remote hosting, and it will support up to 60 different products for sale. Our cart does work on Wordpress sites, there is a user-created plugin that will simplify the process of adding our buttons to your site: