On a major website that gets thousands of views? I don't think so. The scalability of that would be horrible.
No, they are not using flat files. If they are, they are really stupid.
I don't see why anyone would want to use flat files these days when the infrastructure and tooling is so effortless to make use of a real database. It would actually be harder to create programs to read/write in flat files now, not easier. With Rails, Grails, Django and Roo... why would you? It's even easy to do it with old-school Spring and other older technologies as well.
Again, unless your totally incompetent, using the database and fixing this problem would have been really simple. I don't buy it.