As a chemistry major (in Texas, just like Rand Paul), I hung around with a lot of pre-meds. I knew two pre-med students who got into medical school after three years of college. That was far from the norm, they had to be truly exceptional with perfect grades, a very high score on the mcat, a great interview with the med school, etc. They practically had to walk on water. After they earned their MD, the university then counted the medical degree time towards the remaining year of their undergrad studies and officially gave them their BS.
I wonder if Baylor did the same? That would make the wiki reference correct — he DID leave before getting his BS, but that doesn’t mean he was eventually credited with one by Baylor after he graduated with his MD. We would have to know if this was the policy of Baylor at the time to know whether or not he has an undergraduate.
Disclaimer: I am not an apaulogist; he is not my candidate. I just know it is possible (or at least was possible when I was in university) to get into medical school after three years, without a bachelor’s degree, and then have the more rigorous curriculum of med school accepted three years later as the final year of credit towards the BS. Those folks got their MD before they were awarded their BS/BA!