I'm in the UK my understanding is a bachelor's is a synonym for an undergraduate degree; so why did you use the different terms here?
Ah, I think I see it: you copied from Wikipedia; wherein it says he did a bachelors degree in Economics (BA?) and a further bachelors in physics (BS/BSc) whilst he was a graduate. Two undergraduate degrees.
Other sources suggest he did the degrees coterminously:
>"Musk graduated from UPenn in 1994, with double bachelor degrees in Physics (from the College of Arts and Sciences) and Economics (from the Wharton School)." (http://studyadvantage.co/elon-musk-education-study/)
That sources says he had 2 days in a PhD program.
https://www.wharton.upenn.edu/academic-programs/ suggests he did what they call a "dual degree". Making Wikipedia wrong, he didn't "stay" for his second degree he did the two together.
I tried my hand at googling this but found nothing but re-hashes of the same story of how he left after two days.
Watch the video of Sal Khan(fron Khan Academy) interviewing Elon musk.
I second the recommendation of watching the interview. There is way too much misinformation surrounding Tesla and Elon Musk.
My guess would be that you aren't technically in the PhD program until you've passed your qualifying exam. Until that point, you're a graduate student but not a PhD student. After you pass your preliminary exam, you're a PhD/Doctoral candidate.
Also, it's a moot point. There are no bragging rights to be found in simply being admitted to a PhD program. Plenty of very intelligent people fail to complete a PhD program (usually, IME, because of personality issues/conflict with the advisor (sadly extremely common), inflexibility of the advisor and/or department, or personal reasons (economic, social, health)).
(to be clear, Musk didn't brag that he was admitted to Stanford - he suggested that he felt dropping out was more useful than continuing. His fans often hold up being admitted to a PhD program as evidence of his engineering background)
Which background is that? He has an undergraduate degree in economics and a bachelor's degree in physics.
I respect the guy but he clearly puts a lot into managing his image. As a relevant example, he used to claim to have been in the Ph.D. program at Stanford, but had to retract that (I leave it as an exercise to the reader to find that on Google).