Correct. Running database servers don't like file-level backups. If you do this, it's basically luck as to whether the backup of the database server would work when restored (on a good day, it'll work, on a bad one, it'll either refuse to start at all, or it will start with missing data or databases that are marked as crashed).
When backing up a running database server, you have to back it up using software that understands it's a database server. Software designed for this will be able to tell the server it's being backed up, so the server can do things like unload a database's files and flush them to disk, or produce a dedicated copy of the database that can be backed up safely.
If you don't use such software, your choices for safe backups are generally to either dump the databases (e.g. mysqldump) and back up the .sql file, or stop the database server and make normal backups of the server's files.