Ignore the number of hearts — you make a great point!
I found that image here: http://www.mindtheproduct.com/2011/10/what-exactly-is-a-product-manager/ for some more context.
The combination of technology and business model and design (call it interaction or visual or whatever) are what hold a holistic user experience together. That said — you can make a wonderful user experience on top of mediocre technology and no business model (Twitter at the beginning was not excellent technology though it sure is now) and still have a great product so I think the Venn diagram does hold some value.
But ultimately — we are all responsible for producing a fast and usable user experience