Yes, he can. While he has the option to present it in private, it is his call. Award presentations are not only about you. Your commander probably understands the importance of publicly recognizing members of the team. AR 600-8-22, para 1-32g states:
Whenever practical, badges will be presented to military personnel in a formal ceremony as provided in FM 3–21.5. Presentations should be made as promptly as practical following announcement of awards, and when possible, in the presence of the troops with whom the recipients were serving at the time of the qualification
