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Yes, he is right. Since it is a perforation by a clean mode, that is by earbuds, even antibiotics drops are not required at this moment. Just care to be taken to avoid infection, which most commonly occurs by water entering into the ear.
Tympanic membrane injuries heal within four weeks in a majority of the cases. The sound and minor hearing loss will recover as it heals. Also, you should get repeat ear examination done after four to five weeks to confirm if it has healed or not. If you notice any ear discharge in these four weeks, then antibiotic ear drops need to be started to tackle infection.
Hope this helps you and get back if you have any doubts.
For more information consult an internal medicine physician online.