I seem to remember that Nintendo screwed Sony over due to the terms of the contract that Sont wanted and then went with Philips instead for their CD drive, all this without telling them and Sony only found out when Nintendo announced their new partnership with Philips on Stage. The Playstation was born out of no small amount of spite, it would seem. I bet that this is a decision that Nintendo have regretted more than once through the years and it ended up changing the industry forever.
Nintendo didn't screw Sony. Sony wanted nearly all control and profits. After the PS project with Nintendo it basically was canned. Ken wanted to keep it alive but the final product is using the specs SEGA of America proposed to Sony. Had Nintendo used Discs and Saturn was not so poorly designed PS1 would have been a footnote inhistory. PS1 only had success because SEGA made a system impossible to develop for and N64 used carts. PS4 became a success out of the gate because MS and Nintendo messed up not much more to it than that.
If you start negotiations on a contract for hardware and then decide to pull out and join another partner without telling the previous one and then proceed to drop this bomb on stage; that's screwing someone over. No two ways about it. And yes, Sony wanted to make money off of this, they were a huge deal in formats, movies and music and their distribution channels alone were easily worth the cost, it wasn't really such an unreasonable demand for what they would have brought to the table. Your second sentence is also a bit funny when you think about Nintendo's own policies towards 3rd parties in the 80's and early 90's. They were now faced with having use of someone with influence and platforms into markets they wanted to access and they needed to forsake some profits and control to get there, but felt that this was really unfair, despite their own Hitler-esque tactics employed against both developers and retailers for about a decade. It's a special kind of irony, this.
PS1 being a footnote in history if N64 had disc and Saturn was simply better designed is simply speculation, it's highly unlikely that it would have been irrelevant. It brought 3D fighters to the fore with titles like Tohshinden and Tekken, it had the arcade crowd appeal with titles like Ridge Racer and Wipeout, it even had computer fans excited with titles like Road Rash, Warhammer, later Diablo and similar fare and it had more childproof games like Jumping Jack Flash. Great platformers, action titles, racing greats like Need for Speed and some really good RPG's and ARPG's to top it off. This wide appeal wouldn't have gone away even with stronger competition and with decent pricing and hardware as well as CD audio and FMV capabilities, it's really hard to make arguments making it a "footnote in history", perhaps even impossible.
The PS4 also carried the flag of three successful consoles before it, the worst of which sold about 90 million, so to attribute its success solely to the failings of MS and Nintendo is grossly inaccurate by all logic. It doesn't innovate or surprise or go anywhere unexpected at all, and this is exactly why it's selling like it is. Placid and safe, a decent business proposal but not hugely exciting for old, grizzled gamers like myself, but that's a different matter. Even if I'm not over the moon about a product, that doesn't mean I can't respect what it accomplishes or that I should disregard its merits as they stand.