You are correct. My TiVo Series 4 is provided by my cable company and it searches across all sources of video whether it be broadcast, Netflix, Amazon, my cable company's own on-demand service, etc. I search for, say, a movie and it tells me it is available on Netflix but not Amazon, and lists prices (if applicable) and you choose the source you would prefer to watch from.
As far as the preferential searching goes, I have never seen that, but it's nice being presented with a list of sources where that specific movie is available from and the relative pricing (e.g. rent on Amazon or from cable-co on-demand, or 'free' on Netflix with subscription)