That's obviously false. If you send a rocket outside solar system (as in giving it exactly the escape velocity) then you just wait until it's velocity with resp

That's obviously false. If you send a rocket outside solar system (as in giving it exactly the escape velocity) then you just wait until it's velocity with respect to sun drops close to zero and then just nudge it back directly at the sun. This takes a lot of time of course, but it does not require you more energy than what is required to leave solar system. I am only picking at you because you mentioned a rocket. If you said "shoot it to burn in sun" then you would be (mostly) right.