Crowding to kiss the Black Stone, and its virtue

It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that he would push forward through the crowd to reach the Black Stone, and when the people saw him they would make way for him out of respect and widen the space for him.
Imam Nafi' (may Allah have mercy on him) relates: Once I too was caught in this severe crowding of the people. A man struck me with his elbow from behind, the pressure of which made the man in front of me fall, and I too fell backwards. At that moment I began to fear that I would not return safely, but that this crowd would crush me to death. Yet despite all this, Sayyiduna Ibn Umar (may Allah be pleased with them both) insisted on pressing forward to reach the Black Stone.

Imam Abu Dawud al-Tayalisi (may Allah have mercy on him) narrates that it was the practice of the Commander of the Believers, Sayyiduna Ali bin Abi Talib (may Allah be pleased with him), that whenever he passed by the Black Stone and found people crowding heavily there, he would (instead of kissing it, because of the crowd) face towards it, proclaim the greatness of Allah, and recite this supplication: 'Allahumma imanan bika wa sunnati nabiyyika' (O Allah, (I do this) purely out of faith in You and in following the Sunnah of Your Prophet).

It is narrated from Sayyiduna Abdullah bin Amr (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) said: "Had it (the Black Stone) not been touched by the impurities and filth of the Days of Ignorance, no one afflicted with an illness or ailment would touch it without being cured; and on the face of the earth there is nothing from Paradise other than it (the Black Stone)."

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that he said: "Indeed, this corner of the Ka'bah is the right hand of Allah Almighty on the earth, with which He shakes hands with His servants just as a man shakes hands with his brother."
This report is mawquf, and its chain is sahih (authentic).

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that the Prophet (peace and blessings be upon him) said: "An angel descended (from the heaven) along with the Black Stone."

It is narrated from Sayyiduna Abd al-Rahman bin Awf (may Allah be pleased with him) that he related: The Prophet (peace and blessings be upon him) asked me: "What did you do regarding the istilam (kissing or touching) of the Black Stone?" I said: "(When I had the chance) I did the istilam, and (because of the crowd) I also left it." He (peace and blessings be upon him) said: "You did right."
The narrators of this hadith are thiqat (trustworthy), so if Urwah's hearing from Sayyiduna Abd al-Rahman bin Awf (may Allah be pleased with him) is established, this report is sahih (authentic). Imam al-Shafi'i (may Allah have mercy on him) explained its meaning as: he left the istilam when there was a crowd, and did the istilam when there was no crowd.

Manbudh narrates from his mother that she related: I was with the Mother of the Believers, Sayyidah Aishah (may Allah be pleased with her), when one of her freed slave-women came and said: "I did the istilam of (kissed) the Black Stone three times during the seven circuits of tawaf." Sayyidah Aishah (may Allah be pleased with her) (expressing strong displeasure at this act) said two or three times: "May Allah not reward you for it! Why did you not say 'Allahu akbar' (Allah is the Greatest) from a distance, gesture, and pass by quietly? You intended to push into the crowd of men and jostle them (which is wholly unbefitting for a woman)."
According to the commentators of hadith, this fiqh principle is derived from this report: kissing the Black Stone is recommended for women only when there is no crowd of men; otherwise mixing with unrelated men and bodily contact with them would amount to taking the path of disobedience to attain a virtue. Therefore in such a situation, gesturing from a distance is the Sunnah and a means of reward.