Generally, anytime you see "unknown field" in an SQL error, it means that table doesn't exist, or a new field that was supposed to get created, wasn't, and that's a fault of the Update or Install function in the .install file.

The reason your workaround "works" is because both the uc_file_products Contrib, and the core uc_file module, both use a table called uc_file_products. This was mentioned by Shawn when the core module was first introduced. It seems like you need to not just disable modules (such as the File Products contrib) but uninstall them altogether. Uncheck them from your admin/build/modules menu, and then click the Uninstall tab, and click Uninstall. You might even consider deleting the files off your server, in case they are still getting called for some wonky reason.

If that doesn't work, get into phpMyAdmin and remove the uc_file_products table manually, and reinstall the core module.