salaam desertbird,
The declaration at Ghadeer is defenately not a lie as it is one of the most narrated event of the Islamic history. You may wish to disagree with the interpretion of the event which you have a right to. For details you could search this forum and there has been plenty of debates about it before.
Secondly, you said that Quran does not mention anything explicitly as to how to chose a leader. I beg to differ as Quran clearly says that the right to chose a leader belongs to Allah (swt) alone and not the people (Sura Qasas 28:68). For example, story of Talut is in reasonable detail in the Quran (Sura Baqarah: 246, 247). Hence creation and legislation is by Allah's will alone and man has no choice in either of these fields.
Thirdly, i would like to clarify the methods you mentioned were used to chose the first 4 khalifas:
1- Hz Abu Bakar was nominated at Saqifa not by majority but by just 3 influential muhajirs and a party of Ansar who did not entirely agree with his appointment either (Sahi Bukhari has some details if you wish to read more)
2 - Hz Umar was nominated by Hz Abu Bakar and not chosen by the people.
3 - Hz Umar made a comittee that picked Hz Usman as the Khalifa. Remmember that Ibn Awf, the cousin of Hz Usman, was given a kind of veto power over the other members of the committee that included Imam Ali.
4- For a month or more the seat of Khalifa remained empty and arguments grew inside masjid e Nabawi where people had gathered to chose a leader until mass of people decided to go to Imam Ali house and said not to leave until he accepts the office. I guess they knew that he was the only one who had such tremendous and unmatched personal strength as to be able to handle the situation people found themselves in. Imam Ali reluctantly took it despite the grave situation of the time. However what happened next could be read in the history books. Prophet (saww) had foretold Imam Ali of the hard tests he was to face after his departure and Imam Ali showed great resolve and patience in the worst of times.