The thing is if two of you have the same birthday then it falls on the same day . But if two of you have the same face, that doesn't mean you have to use the same phone. So unlike the birthday paradox where your birthdays "clash", you'd still have to try everyone's face on everyone's phone.

An actual Birthday Paradox equivalent would be if you had 1,000,000 phones and the 1,179 people in the auditorium, and you assigned people to a phone based on their face recognition ID. Then you would get your high chance that not everyone would get a unique phone.