Premedical Sciences and Basic Sciences are 2 different animals.
I would imagine one could feasibly piecemail thier pre-medical requirements through distant learning by taking inorganic chemistry, organic chemistry, physics, biology, anatomy, phsyiology, microbiology and so forth at various universities across the nation. The problem would be if the medical school would accept those courses without a lab component. The University of Utah offers some of those courses online as well as the University of Oklahoma. Harvard has "an extension campus" for pre-med but I don't believe it is online.
Overview : Harvard Extension School

There has been some discussion on this forum in regards to "online medical school" of which the basic sciences were given in part online but the clinical rotations were at affliated hospitals. Schools such as IUHS of St. Kitts, Oceania of Samoa and UHSA of Antigua might still offer some of the courses via distant learning but licensure issues in the USA have been brought up. Whether or not those schools are accredited I don't know but they are listed in the IMED directory found at:
IMED - FAIMER International Medical Education Directory

Make sure you check with the medical school you are applying to if the online premedical courses are accepted!!!!