Also from WWM:
Treatment is unnecessary if you select a healthy, clean specimen and provide a suitable habitat. The usual two to three week quarantine for newcomers is recommended. Stay away from copper compounds and the organophosphate DTHP (masoten, dylox, Dipterex, Neguvon...) containing remedies; these are deadly to true eels. If your specimen(s) seem to be developing a bacterial and/or fungal infection, check water quality, do a massive water change, or remove them to a treatment tank and treat with the antibiotic erythromycin (Maracyn) to reduce overall bacterial levels.
Don't fret too much if your eel goes on a hunger strike. Morays collected in the wild have empty stomachs and can go for long (months) without eating.
Sounds to me like the reason to QT an eel is more to get it accustomed to eating and to observe it. They don't usually get sick or carry any parasites.