You mean, 1st wipe all old backups at iTunes and take a new backup and then restore ?
No, I believe they mean restore the phone to factory, set up as new. iCloud will bring in your contacts, etc and then manually reinstall your apps. That's the only way to get a fresh install. If you have something corrupted in your OS and restore from a backup, the bug is likely to come back along w the backup. The backup essentially creates a snapshot of your iPhone, so backing up in that state and then restoring from it is not likely to resolve your issues.
If you must, migrate photos etc off first or use iCloud Photo Library if you have the space. Believe me, it sounds nuts but restoring from recovery mode (fresh download/install of iOS) and setting up as new will really work wonders for these types of software glitches. I resolved some bugs that had plagued me across several versions of iOS by doing this earlier this year.