The Gemara says that the נ"מ is whether or not he can give to his wife and children. The Tur raises the question, what about if he picks it up to eat himself and then decides to give it to his wife or children (even if משמים הוא אוכל)? The Tur has 2 opinions and rejects the opinion that it is permitted. The Gra on Shulchan Aruch says that the 2 opinions are based on a machlokes Rashi and Tosafos. Rashi says "כל זמן דלא מטי לידיה לא זכי ליה". The implication is that once he does pick it up it his to do what he wants with including giving to his wife and kids. Tosafos however, says that he is not זוכה until he is "לועס ואוכל" which means that he cannot give it to his wife and kids.
In truth, Rashi on ד"ה אינו קוצץ) עמוד ב ) seems to say like Tosafos "דאין לפועל קטן זכות אלא שנותן לתוך פיו"
Also, in truth, Tosafos is a bit of a פלא, why should he only be זוכה when he puts it in his mouth? Why should this be different then any other מתנות עניים?