That's not quite true. In certain circumstances perhaps because he knows the Hondas all work better on a harder tyre, but Rossis own strength over others on similar bikes like Maverick or Lorenzo in the past is his strength in braking as can be seen by his many passes after the main staights at both Mugello and Assen so he also benefits from a stiffer carcass.
I dont know if they used it at Assen but Rossi, Maverick and Marquez all benefited from the assymetric tyre they tested after Barcelona.
Edit - just seen you say the Ducati years; I'm guessing at that time he would certainly do anything possible to get an edge over the competition as he was struggling so much. I dont think it made much difference anyhow, these little advantages only really count when things are very close like they are in the championship at the moment, but there doesn't seem to be a clear cut advantage that Rossi can choose over the competition anyhow as things change so much between tracks and weather conditions. The Yamaha this year with the Michelin tyres seems to prefer hard at one track and soft at another, whereas the Honda pretty much always wants comparatively harder tyres.