Nothing is impossible. In California, students can sit for the FYLSE and, ultimately, the California bar simply by studying the law in a judge's or attorney's office. A superbroke (like me), but really motivated student can enroll in Mid-Atlantic, read, and brief, at least 25 cases of the court opinions cited in each Gilbert's volume, do an internship or write a book synthesizing a legal issue and petition the California Supreme Court to show it what the student can do. There are many court opinions written by the courts of several state supreme courts discussing the very issue of the petitioner seeking to take that state's bar exam because the student had not attended an accredited law school. Read the case law.
The petitioner will have a pretty tough burden of proof because Mid-Atlantic is not accredited. But, the petitioner will have meticulous notes demonstrating that he/she has acquired the necessary knowledge. And, his/her very petition and oral argument before the court will hint at actual proof that he/she has what it takes to be an attorney.