There's plenty of politics and arbitrariness to Nobel prizes (especially in non-science prizes, eg giving Obama or Malala the peace prize), which probably makes it less of an issue that there may be some politicking within the small group of potential laureates since who among them actually wins is relatively arbitrary.

Eg since only 3 people can win a prize, you can have cases like Francois Englert and Peter Higgs winning the prize for the Higgs Boson despite 4 other scientists having published papers on the same thing around the same time, and the scientists at the LHC who actually confirmed its existence.

Similarly, a work can have won a prize, but if one of the authors passes away before the nomination is made, that person misses out on the title.

> then wouldn't that also apply to the prizes at the top?

It does, but the politics and favoritism is happening within a heavily selected group of very, very competent people. Plenty of people get snubbed for petty reasons, but they get snubbed in favor of others who are also doing Nobel-worthy work.