What's crazy about his writeup is he never defines the word "product picker". He just uses it:

When I was an Entrepreneur in Residence at Benchmark Capital, I often heard the partners use the term "Product Picker." A team might come in to pitch, and the partners would ask, after the meeting, "which of you is the Product Picker?"

I take his lack of definition to mean: the Product Picker is the person with final say of what the product is.