No, I don’t think a student has to have 3 sciences HL to be prepared for pre-med. My D who is going to med school took HL Biology and SL Chemistry. The highest math she could get before graduation was SL Mathematics, so she took Calc I at a CC before she left for college.
I think the biggest reason IB was good preparation for pre-med wasn’t so much the content but that she learned how to write well, she learned how to research, she learned how to think critically and look at things from other points of view, and to successfully make it through IB she had to develop some kick butt study skills. She attends a pretty rigorous liberal arts college. Hundreds started out as pre-meds, many shining stars in their high school. But many had too steep of a learning curve for college level work, and weren’t premed for too long. Both my Ds hit the ground running, with no learning curve for how to study, write papers, and take non-multiple choice tests. I remember my older D had a course her freshman year in which they had to read and analyze difficult texts on political thought. Some students were blown away, but my D had no problem, she had done this numerous times in IB History of the Americas and TOK.