What Apple did was to sit in the middle of all of the publishers and offer them a platform that would comply with their demands. Before Apple's involvement the publishers did want to conspire regardless, but they had no way to fight with Amazon. It was unpalatable to them to lose so many sales in order to try and move prices up.
Apple provided the iPad, which would comply with their demands and undoubtedly be incredibly popular. They did this knowing full well that it would eliminate retail price competition and so put their platform in a perfect place to sell to their users. Why would anyone install a Kindle app if the prices were exactly the same?
This is what Apple did that was illegal, they were involved in orchestrating a conspiracy to eliminate price competition which would directly benefit them. It's a long read, but http://www.justice.gov/atr/cases/f299200/299275.pdf summarises it pretty well.
Are you writing this in your imagination? Kindle app opens the books bought from Amazon. How could the prices be exactly the same as from the iBook store?