The big difference between flat-file and database backed forum systems is that the load for accessing the file system and doing all the nasty bits get shifted to the database server. There are several other things that make a database backend better, but it is possible to run large boards on a flat-file based system without many problems.
I won't lie: in many cases database backed systems perform better; however, it doesn't really matter unless you have a very popular board with lots of posts, activity, etc.