“Nobody said that a written source has no validity, we’re just arguing that an unwritten one can, too. What do we do when there’s a conflict between written sources?”
The difference between a conflict amongst written sources and a conflict between written sources and oral sources is that (generally speaking) if you see a written source from rishonim for example, you can be confident that you have in front of you the opinion of the rishonim. But when your source is oral, there is a very good chance that over the hundreds of years, something was lost/added/mixed up as indeed has happened to many things.