The train companies went to the US government and said "bail us out or we all go out of business". So the senate created Amtrak as a private company, and purchased all of the money losing assets (all passenger routes) from the train companies. The US government owns all voting shares, and the train companies owns all non-voting shares. So Amtrak is a quasi public-private utility companies, where the cost is bore by public in tax money.
Here is the kicker, the special interest group that lobbied for the US government to create Amtrak was ... the US airlines. They bet that passenger trains would be obsolete in a few decades, so the tax payers would not be holding the bag for too long.
50 years later, we are still holding the bag. According to my sources, they will be break even across all routes in a couple of years. By the way, all passenger trains in Europe , China and Japan lose money too.