Being a Rhodes Scholar is considered super prestigious. Especially if you are from the US (where there is heavy competition for this), this will carry a lot of cache...probably more than working in some NIH lab...residency applicants who worked in someone's lab are a dime a dozen. If you publish something in Nature or Science and you are the first author, that may be different.
Some of these other scholarships that are not well known may not "help" you as much to get into a residency as doing productive bench research work. However, just because you get into someone's lab at NIH, even if it's a pretty well known person, does not mean that you are going to get your name on a lot of research papers. Also, getting your name on a couple of papers as an "et al." isn't going to make or break your medical career.
Competing for and obtaining a difficult-to-get scholarship like Truman, etc. would probably help w/the med school applications process. It will give you something to talk about @residency applications time, but what will really get you into a highly competitie residency is getting really high grades in med school and getting letters of recommendation from someone well known to the people doing the picking/choosing of residents, along with a high USMLE Step 1 score.
