You are correct about the Adreno 200 being a trimmed down version of the Xenos GPU from the XBox 360. That shipped before the acquisition by Qualcomm.
However, I can also confirm that the GP is right: Adreno 300, which is the first product that we shipped after the acquisition, combined the fixed-function blocks from AMD with the programmable shader processor (SP) from Qualcomm. That SP had a prececessor (QShader) which had never shipped commercially.
Overall, I think it is inaccurate to say that Adreno is basically AMD's IP. It was the combination of both teams, plus the people who had been previously acquired from Bitboys. This amalgamation of people led to a ton of internal conflict, eventually leading to the closure of the offices staffed by Bitboys and the departure of a bunch of other senior people.
Things are way better these days, or so I hear.