First of all, "concurrent filesystem" is not a standard industry term. I'm not sure such a thing exists, unless you're talking about distributed filesystems. So I'll assume you mean instead concurrent file access at the filesystem level.
Filesystems usually deal with concurrency by using locking (i.e. by NOT dealing with concurrency). That is, it's assumed that if I'm writing to a file, then no one else will be writing to the same file at the same time. If you want to forgo locking, then you're presumably accepting the consequences, and presumably dealing with your own concurrency.
Remember that a filesystem really only guarantees the integrity of the filesystem itself, NOT the integrity of your files. If your files get munged, then that's your fault. The FS only says that it won't be the source of your troubles; not that you won't have any of your own fault.
The elements that the filesystem will protect include directory entries, file permissions and metadata, allocation maps, and many such things that you don't care about. And the fact that you don't have to care about them shows that the filesystem is working correctly.
Note that filesystem journals COULD theoretically be used to protect file contents to a certain extent. But the overhead would be unsustainable, and the performance abysmal.