Hi Kad,
this would be a very logical answer if the cheikh happened to be the only person who understood as such. But he is not, and based on sound tradition. What you gave is a the version of Muhammad Ibn Umar, or best known as Al-Wakidi who is notorious for thousands of false hadith.
Zainab daughter of Abu Salama reported: I heard Umm Salama, the wife of Allah’s Apostle (may peace be upon himy, saying to 'A’isha: By Allah, I do not like to be seen by a young boy who has passed the period of fosterage, whereupon she ('A’isha) said: Why is it so? Sahla daughter of Suhail came to Allah’s Messenger (may peace be upon him) and said: Allah’s Messenger, I swear by Allah that I see in the face of Abu Hudhaifa (the signs of disgust) on account of entering of Salim (in the house), whereupon Allah’s Messenger (may peace be upon him) said: Suckle him. She (Sahla bint Suhail) said: He has a beard. But he (again) said: Suckle him, and it would remove what is there (expression of disgust) on the face of Abu Hudhaifa. She said: (I did that) and, by Allah, I did not see (any sign of disgust) on the face of Abu Hadhaifa. (Sahih Muslim, Book 008, Number 3428)
umm Salamah wasnt weaning children and so had no milk to offer which means Aisha’s advise was not about putting milk in the cup but actual breast suckling.
Ibn Abu Mulaika reported that al-Qasim b. Muhammad b. Abu Bakr had narrated to him that 'A’isha (Allah be pleased with her) reported that Sahla bint Suhail b. 'Amr came to Allah’s Apostle (may peace be upon him) and said: Messenger of Allah, Salim (the freed slave of Abu Hudhaifa) is living with us in our house, and he has attained (puberty) as men attain it and has acquired knowledge (of the sex problems) as men acquire, whereupon he said: suckle him so that he may become unlawful (in regard to marriage) for you He (Ibn Abu Mulaika) said:** I REFRAINED FROM (narrating this hadith) FOR A YEAR OR SO ON ACCOUNT OF FEAR.** I then met al-Qasim and said to him: You narrated to me a hadith which I did not narrate (to anyone) afterwards. He said: What is that? I informed him, whereupon he said: Narrate it on my authority that 'A’isha (Allah be pleased with her) had narrated that to me. (Sahih Muslim, Book 008, Number 3426
Here was a man who was afraid to narrate what he had heard and decided to keep this story to himself for more than a year. Was he afraid fom the idea of putting some milk in a cup?