Yes, the logic does transfer. In fact, it is a little known secret that Harvard med students get a big gold sash to wear to their residency interviews. This sash is a subtle hint to the residency director to skip the interview and automatically offer this student a spot in next year's intern class. Clearly, this Harvard student worked SO MUCH harder to become an MD than any of the other people interviewing that day, so he automatically deserves a spot.
(Sigh.) Look, threads like these are kind of insulting and sort of pointless. Everyone who goes to med school has to work hard to stay in and finish successfully, regardless of which school they go to.
The main point of your question seems to be asking about the importance of student-student competition - i.e., is it harder to do well at a higher ranked school because the competition between students should be that much more fierce? Since so many schools are now H/P/F and do not use a curve, the element of competition between students is no longer important. That's WHY so many schools switched to this grading system - the point was to create an atmosphere that fostered teamwork, not cutthroat competition. Furthermore, most schools do not numerically rank their students - they just say that you were top third/top 25%, etc. How well you do and how high you pass is now dependent almost solely on you. I guess you could argue that there's more ambition among the students at a big-name school, but that's debateable and there's no evidence to prove it.
Really, these kind of threads are sort of insulting. It implies that students who are currently at state schools are kind of coasting on the way to becoming MDs because the bar is lower. (Before you jump down my throat, I know that you didn't mean to be offensive - that's just how it sounds to me, and I don't even go to a state school!) Everyone has to work hard to finish med school, end of story. I doubt that I'd have more free time at a lower ranked school, and I'm not sure how I'd be able to have less free time at a higher ranked school.
Finally, a word of caution when applying to med school. Don't assume that students at higher ranking schools are intrinsically more capable than people at lower ranking schools. There might be some truth to that assumption, but there ARE a lot more external factors in deciding where to go for med school than there are in deciding where to go for undergrad. A lot more people in med school are married and have families, so going to a really expensive Ivy League school is out of the question for them, even if they were to get in. Some people choose to go to a school close to home so that they can save some money by living with their parents. In their case, going to an expensive med school just defeats the purpose. It's a much more complicated decision than deciding where to go to college.