Are the dead punished for the weeping of their relatives?

In the below Hadith, Umar stated a false Hadith that was disputed by Aisha, who corrects the statement by using the Quran. This shows that the companions themselves could be wrong on what they think they heard the prophet state, and that the source of truth should always be the Quran

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حَدَّثَنَا عَبْدَانُ، حَدَّثَنَا عَبْدُ اللَّهِ، أَخْبَرَنَا ابْنُ جُرَيْجٍ، قَالَ أَخْبَرَنِي عَبْدُ اللَّهِ بْنُ عُبَيْدِ اللَّهِ بْنِ أَبِي مُلَيْكَةَ، قَالَ تُوُفِّيَتِ ابْنَةٌ لِعُثْمَانَ ـ رضى الله عنه ـ بِمَكَّةَ وَجِئْنَا لِنَشْهَدَهَا، وَحَضَرَهَا ابْنُ عُمَرَ وَابْنُ عَبَّاسٍ ـ رضى الله عنهم ـ وَإِنِّي لَجَالِسٌ بَيْنَهُمَا ـ أَوْ قَالَ جَلَسْتُ إِلَى أَحَدِهِمَا‏.‏ ثُمَّ جَاءَ الآخَرُ، فَجَلَسَ إِلَى جَنْبِي فَقَالَ عَبْدُ اللَّهِ بْنُ عَمَرَ ـ رضى الله عنهما ـ لِعَمْرِو بْنِ عُثْمَانَ أَلاَ تَنْهَى عَنِ الْبُكَاءِ، فَإِنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ ‏"‏ إِنَّ الْمَيِّتَ لَيُعَذَّبُ بِبُكَاءِ أَهْلِهِ عَلَيْهِ ‏"‏‏.‏ فَقَالَ ابْنُ عَبَّاسٍ ـ رضى الله عنهما ـ قَدْ كَانَ عُمَرُ ـ رضى الله عنه ـ يَقُولُ بَعْضَ ذَلِكَ، ثُمَّ حَدَّثَ قَالَ صَدَرْتُ مَعَ عُمَرَ ـ رضى الله عنه ـ مِنْ مَكَّةَ حَتَّى إِذَا كُنَّا بِالْبَيْدَاءِ، إِذَا هُوَ بِرَكْبٍ تَحْتَ ظِلِّ سَمُرَةٍ فَقَالَ اذْهَبْ، فَانْظُرْ مَنْ هَؤُلاَءِ الرَّكْبُ قَالَ فَنَظَرْتُ فَإِذَا صُهَيْبٌ، فَأَخْبَرْتُهُ فَقَالَ ادْعُهُ لِي‏.‏ فَرَجَعْتُ إِلَى صُهَيْبٍ فَقُلْتُ ارْتَحِلْ فَالْحَقْ أَمِيرَ الْمُؤْمِنِينَ‏.‏ فَلَمَّا أُصِيبَ عُمَرُ دَخَلَ صُهَيْبٌ يَبْكِي يَقُولُ وَاأَخَاهُ، وَاصَاحِبَاهُ‏.‏ فَقَالَ عُمَرُ ـ رضى الله عنه ـ يَا صُهَيْبُ أَتَبْكِي عَلَىَّ وَقَدْ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏"‏ إِنَّ الْمَيِّتَ يُعَذَّبُ بِبَعْضِ بُكَاءِ أَهْلِهِ عَلَيْهِ ‏"‏‏.‏ قَالَ ابْنُ عَبَّاسٍ ـ رضى الله عنهما فَلَمَّا مَاتَ عُمَرُ ـ رضى الله عنه ـ ذَكَرْتُ ذَلِكَ لِعَائِشَةَ ـ رضى الله عنها ـ فَقَالَتْ رَحِمَ اللَّهُ عُمَرَ، وَاللَّهِ مَا حَدَّثَ رَسُولُ اللَّهِ صلى الله عليه وسلم إِنَّ اللَّهَ لَيُعَذِّبُ الْمُؤْمِنَ بِبُكَاءِ أَهْلِهِ عَلَيْهِ‏.‏ وَلَكِنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ ‏"‏ إِنَّ اللَّهَ لَيَزِيدُ الْكَافِرَ عَذَابًا بِبُكَاءِ أَهْلِهِ عَلَيْهِ ‏"‏‏.‏ وَقَالَتْ حَسْبُكُمُ الْقُرْآنُ ‏{‏وَلاَ تَزِرُ وَازِرَةٌ وِزْرَ أُخْرَى‏}‏‏.‏ قَالَ ابْنُ عَبَّاسٍ ـ رضى الله عنهما ـ عِنْدَ ذَلِكَ وَاللَّهُ هُوَ أَضْحَكَ وَأَبْكَى‏.‏ قَالَ ابْنُ أَبِي مُلَيْكَةَ وَاللَّهِ مَا قَالَ ابْنُ عُمَرَ ـ رضى الله عنهما ـ شَيْئًا‏.‏

Narrated Abdullah bin 'Ubaidullah bin Abi Mulaika: One of the daughters of Uthman died at Mecca. We went to attend her funeral procession. Ibn Umar and Ibn Abbas were also present. I sat in between them (or said, I sat beside one of them. Then a man came and sat beside me.) Abdullah bin Umar said to Amr bin Uthman, "Will you not prohibit crying as Allah's Messenger (ﷺ) has said, 'The dead person is tortured by the crying of his relatives.?" Ibn Abbas said, "Umar used to say so." Then he added narrating, "I accompanied Umar on a journey from Mecca till we reached Al-Baida. There he saw some travelers in the shade of a Samura (A kind of forest tree). He said (to me), "Go and see who those travelers are." So I went and saw that one of them was Suhaib. I told this to Umar who then asked me to call him. So I went back to Suhaib and said to him, "Depart and follow the chief of the faithful believers." Later, when Umar was stabbed, Suhaib came in weeping and saying, "O my brother, O my friend!" (on this Umar said to him, "O Suhaib! Are you weeping for me while the Prophet (ﷺ) said, "The dead person is punished by some of the weeping of his relatives?" Ibn Abbas added, "When Umar died I told all this to Aisha and she said, 'May Allah be merciful to Umar. By Allah, Allah's Messenger (ﷺ) did not say that a believer is punished by the weeping of his relatives. But he said, Allah increases the punishment of a non-believer because of the weeping of his relatives." Aisha further added, "The Qur'an is sufficient for you (to clear up this point) as Allah has stated: 'No burdened soul will bear another's burden.' " (35.18). Ibn Abbas then said, "Only Allah makes one laugh or cry." Ibn `Umar did not say anything after that.

Sahih al-Bukhari 1286, 1287, 1288 https://sunnah.com/bukhari:1286