This question could have been put more politely and you could have asked about circumstances of death of the Prophet (صلى الله عليه وسلم) instead of making offensive, far-fetched judgements. I really wish the question is edited.
Coming to the question, if you had been sincere, you would have found the other version of the hadeeth narrating the complete incident.
'Abdur-Rahman bin Abu Bakr entered upon the Prophet (sallallahu
'alaihi wa sallam) while I was supporting the Prophet (sallallahu
'alaihi wa sallam) on my chest. 'AbdurRahman had a fresh Siwak then
and he was cleaning his teeth with it. Allah's Messenger (sallallahu
'alaihi wa sallam) looked at it, so I took the Siwak, cut it (chewed
it with my teeth), shook it and made it soft (with water), and then
gave it to the Prophet (sallallahu 'alaihi wa sallam) who cleaned his
teeth with it. I had never seen Allah's Messenger (sallallahu 'alaihi
wa sallam) cleaning his teeth in a better way. After finishing the
brushing of his teeth, he lifted his hand or his finger and said
thrice, "O Allah! Let me be with the highest companions," and then
died. `Aisha used to say, "He died while his head was resting between
my chest and chin."
حَدَّثَنَا مُحَمَّدٌ، حَدَّثَنَا عَفَّانُ، عَنْ صَخْرِ بْنِ
جُوَيْرِيَةَ، عَنْ عَبْدِ الرَّحْمَنِ بْنِ الْقَاسِمِ، عَنْ أَبِيهِ،
عَنْ عَائِشَةَ، دَخَلَ عَبْدُ الرَّحْمَنِ بْنُ أَبِي بَكْرٍ عَلَى
النَّبِيِّ صلى الله عليه وسلم وَأَنَا مُسْنِدَتُهُ إِلَى صَدْرِي،
وَمَعَ عَبْدِ الرَّحْمَنِ سِوَاكٌ رَطْبٌ يَسْتَنُّ بِهِ، فَأَبَدَّهُ
رَسُولُ اللَّهِ صلى الله عليه وسلم بَصَرَهُ، فَأَخَذْتُ السِّوَاكَ
فَقَصَمْتُهُ وَنَفَضْتُهُ وَطَيَّبْتُهُ، ثُمَّ دَفَعْتُهُ إِلَى
النَّبِيِّ صلى الله عليه وسلم فَاسْتَنَّ بِهِ، فَمَا رَأَيْتُ رَسُولَ
اللَّهِ صلى الله عليه وسلم اسْتَنَّ اسْتِنَانًا قَطُّ أَحْسَنَ مِنْهُ،
فَمَا عَدَا أَنْ فَرَغَ رَسُولُ اللَّهِ صلى الله عليه وسلم رَفَعَ
يَدَهُ أَوْ إِصْبَعَهُ ثُمَّ قَالَ " فِي الرَّفِيقِ الأَعْلَى
". ثَلاَثًا ثُمَّ قَضَى، وَكَانَتْ تَقُولُ مَاتَ بَيْنَ حَاقِنَتِي
Please the read the complete hadeeth above, especially the bolded part. If you have ever used a siwak you would know that a new one is a bit stiff because of its bark and it needs to be stripped. So before you use it, you strip it by chewing it and moistening it by your saliva or water.
Now, Aa'ishah al-Siddiqah (May Allah be pleased with her), the wife of the Prophet (صلى الله عليه وسلم) chewed it with her mouth so that he could use it. Then the Prophet (صلى الله عليه وسلم) used it. That is what is meant by mixing of the saliva. The Prophet (صلى الله عليه وسلم) loved to use the siwak.
And yes, he (صلى الله عليه وسلم) died near Aa'ishah al-Siddiqah (May Allah be pleased with her) because she was the most beloved person to him (صلى الله عليه وسلم).
Please read more about the death of the Prophet (صلى الله عليه وسلم) here and you can read about siwak here.