What does the story of Buddha's death say about his ultimate beliefs and his integrity of spirits?
The Buddha is the awakened mind which transcends all phenomena. When the Buddha passed into parinirvana at Kushinagara under a pair of shala trees, it was the awakened mind, as liberated spirit, which became free of the deceased carnal body. What of the carnal body (sharira) that remained was called 'Buddha relics' (sharira-dhatu) which were subsequently enshrined in a stupa.
The Buddha, before he passed into parinirvana, told his attendant, Ananda, not to hinder himself by honoring his remains (sharira-dhatu). He said, quoting from The Questions of King Milinda, IV, 3, 25 [PTS]: "Paying reverence is not the work of the sons of the Conqueror, but rather the grasping of the true nature of compounded things, the practice of thought, contemplation in accordance with the rules of Satipatthana, the seizing of the real essence of all objects of thought, the struggle against evil, and the devotion to their own spiritual good. These are things which the sons of the Conqueror out to do, leaving to others, whether gods or men, the paying of reverence [to relics]."
In other words, the Buddha was telling Ananda not to waste his time paying reverence to a corpse, but, instead, to contemplate the true meaning of the teachings, which point the way to "awakening" to the truth of our condition and the means to free ourselves forever from dissatisfaction, unhappiness and suffering.