Avira > Every lther talmid in the world will tell you that he said it was bedieved.
If this were about eruvin, your argument has weight. but about milk – no. One might think that the sons, who are Talmidei Chachamim, were exposed multiple times to situations where milk was discussed at home. Even if they did not halav hacampaniesat home, I am sure there was a simcha somewhere where this was an issue.