If Osama was killed earlier in war on terror, the ignorant Americans may have been skeptical about the official narrative after 9/11. Most citizens have always been ignorant. It is a good form of psychological warfare to keep the death of some enemies hidden to prolong war.
Sacred texts indicate that Solomon peace be upon him was foretold about his imminent death
إن الله عز و جل أوحى إلى سليمان بن داود (عليهما السلام): أن آية موتك
So, he intentionally climbed into the balcony of his palace
قد أحببت أن أدخل قصري في غد، فأصعد أعلاه
People around him thought he was engaged in worship, praying and reciting Psalms
كان يقرأ الزبور و الشياطين حوله ينظرون إليه
Some alternate readings suggest the subordinates were humans
الطبرسي: " تبينت الإنس " و هي قراءة علي بن الحسين، و أبي عبد الله (عليه السلام)
Twelver Tafsir Al-Bahrani
Microsleep is quite common among drivers. So, it seems like an unnoticed dilated microsleep. Although eyes are mostly open at death, but looking at balcony from underneath would not make a noticeable difference.