Seshu - Your case sounds like a very particular one - not something to be generalized. Check out another responsive site: www.waveapps.com. It's a software-as-a-service company that gets new prospects via an online form. Their CTA stays always at the top regardless of scrolling down or switching the device. The same can be accomplished with any other kind of CTA information (phone numbers, emails, etc).
Responsive design does allow for hierarchization and priorization of elements according to each device. Content isn't 'shoved' from one device to the other one. In fact, with responsive design all devices are taken into account before organizing and laying out the content. In fact, mobile is actually a priority for many responsive designers.