I think it sounds like plenty. If she wants to give him more at each feeding, then I would send fewer bottles (i.e. two 6-oz bottles instead). The nanny is thinking of FF babies, who need to increase volume as they get older. BF babies tend to take the same amount from 1 month to 6 months because the milk changes as they grow. My milk is definitely creamier/fattier now than it was when she was 3 months old.
FWIW, my DD has three 6-oz bottles at her babysitter's house, between 8am and 5pm (usually a bottle at 9, 12, and 3), and has done since about 3 months old. We are soon going to try lessening the noon bottle because she eats a bit of solids for lunch now. DD1 had three 5-oz bottles at the same times from the time she was about 3 months until about 7 months (after which we dropped a bottle). To me, 12 oz spread over 5 hours sounds like plenty, no matter how you decide to divide it up.
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