Some narrators used to tell the following story to demonstrate the great importance that the Prophet (peace and blessings of Allah be upon him) attached to prayer or to illustrate the state of the Prophet (SAW) during prayer.

"Once, during a prayer time, the Prophet (SAW) was performing ablution. Meanwhile, Hazrat ‘Aisha  (RA) came beside him, but he did not immediately recognize her. The Prophet (SAW) asked, 'Who are you?' She replied, 'I am ‘Aisha .' The Prophet (SW) asked, 'Who is ‘Aisha ?' She responded, 'The daughter of Abu Bakar.' The Prophet (SW) asked once more, 'Who is Abu Bakar?' ‘Aisha  (RA) replied, 'The son of Quhafa.'

The essence of this story is that when the time for prayer approached, the Prophet would become so deeply absorbed in his devotion that he did not recognize even his beloved wife, ‘Aisha  (RA), or his closest companion, Abu Bakar (RA)."

Surely, the congregational prayer held great importance in Islam.  However, to demonstrate its importance, you do not need to say such baseless things that 'even he did not recognize ‘Aisha  (RA)'. This kind of statements is not found in any reliable sources.

Yes, close to this statement, a weak narrative is available, which is-

كَانَ رَسُوْلُ اللهِ -صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ- إِذَا نُوْدِيَ بِالأَذَانِ كَأَنَّهُ لاَ يَعْرِفُ أَحَداً مِنَ النَّاسِ.

قال الذهبي في سير أعلام النبلاء (في ترجمة سويد بن غفلة) : هَذَا حَدِيْثٌ ضَعِيْفُ الإِسْنَادِ.

"When Adhan (the call to prayer) was called, the Prophet (SAW) turned into as if he did not know anyone."  [Note : Tarikh-a-Dimashq, Ibn Asakir, b.72, p.  367;  Tarikhu Abi zur'ah Addimashqi, b.1, p.660;  Siyaru A’lamin Nubala, b.5, p.29 (The Biography of Suwayd ibn Ghaflah); Takhriju Ahadisil Ihya, Iraqi, Description 387]

There is an authentic hadith narrated by ‘Aisha (RA) herself about how seriously the Prophet (SAW) went to the mosque for prayer after hearing Adhan (the call to prayer). Aswad Ibn Yazid  narrated, I asked ‘Aisha  (RA), what the Prophet (SAW) used to do when he was in the family.  ‘Aisha (RA) replied-

كَانَ يَكُونُ فِي مِهْنَةِ أَهْلِهِ، فَإِذَا سَمِعَ الأَذَانَ خَرَجَ.

He used to engage in family service (helping with family's work). But as  he heard Adhan (the call to prayer), he would go out (to the mosque for prayer). Sahih Bukhari, Hadith 5363

Translation: MD. Arif Billah