These are all theories based off perhaps some very educated guesses, but AFAIK they have never been confirmed by any official or former official from either nvidia or Sony.
Semiaccurate's very accurate article from May claims that neither Microsoft or Sony would even engage in negotiations. If this part is true, then some kind of confrontation must have happened with Sony.
Perhaps Sony wasn't happy that nvidia sold them their 2 year-old GPU architecture while sitting on the brand new G80 architecture with unified shaders that came out at the exact same time as the PS3.
As a comparison, ATi in 2005 sold Microsoft their very first unified shader architecture, which landed on the X360 no less than 1.5 years before ATI's first graphics cards with unified shader GPUs in 2007. And now we know that AMD provided Sony with features for the PS4 that were only seen later in Hawaii cards. And with PS4 Pro they're providing features that won't be in AMD's GPUs until next year, like 2*FP16 throughput.
So regarding Sony, maybe they ended up thinking that nvidia did hide G80 from them. As a matter of fact up until the Geforce 8800 GTX reveal, Jen Hsun kept going on record saying that unified shaders weren't that much better for GPUs, strongly implying that G80 would be yet another architecture with separate pixel and vertex shaders.
I never read Semiaccurate, but every time I hear about it, I get the distinct impression that at some point in the past, Nvidia ran over Charlie Demerjian's dog. What I heard from people inside Nvidia was that at least Sony (and maybe MS, I don't recall clearly) did approach Nv about the new consoles and Nv was kind of an ass in how they said No. As in, went to the meeting, talked about random stuff for a while, then said "Anywaaay... Great to see you. Bye."
What I heard from someone involved in the PS3 GPU process was that the G80 came up in discussions, but it didn't look like it would be ready and solid far enough ahead of the PS3 launch for it it to be a safe bet. Real shame. With a G80 the PS3 would have walked all over the 360. The SPUs would have been useful for a lot more things than just as a crutch for the 7800.