I flipped through a pretty good overview of the history/evolution of the general “interface designer” terms and job titles (props to Funsize, Austin TX) - and came away with the interpretation of ‘product designer’ as one having ability to create an entire interactive ‘product’, from the architecture to visual to interaction behavior and maybe some coding. So yes, the ‘generalist’ title is applicable in this case. The definition of what constitutes a ‘product’ can be a little fuzzy to me tho.