One of those attributes in the title qualifies him to write a scholarly book about Jesus. None of them disqualifies him.
You've perhaps seen the firestorm of controversy regarding the treatment of scholar of religions Reza Aslan in an interview on Foxnews about his book Zealot: The Life and Times of Jesus of Nazareth. He was challenged numerous times about why a Muslim would write a book about Jesus in the first place, to which Dr. Aslan counters that he wrote the book as an historian of religions, not as a Muslim.
Foxnews commentator John Dickerson states that "Aslan is not a trained historian. Like tens of thousands of us he has
been formally educated in theology and New Testament Greek." Dickerson is certainly obscuring the critical issue here. One's PhD does not have to be in "History" specifically to "write as an historian." What Dr. Aslan means is that his book was a scholarly study of an historical person, namely, Jesus, and that he has the necessary credentials to do so. And indeed he does, if you consult his Wikipedia page.
I want to vigorously defend the principle that scholars can explore religious matters outside their own tradition. Indeed, the first academic article I published regarded a long standing controversy in Quranic Studies.
Several Surahs of the Qur'an begin with collections of seemingly random letters, such as "Alif, Laam, Miim (الم)" and "Yaa, Seen (يس)." These so-called "Mystery Letters" of the Quran have prompted numerous explanations.
Despite being a Christian, I studied the matter because I found it interesting. While my PhD minor was Arabic language, I have no formal credentials in Quranic Studies specifically. So someone could just as easily attack my claim to write on such a matter as they are attacking the right of Dr. Aslan to write about Jesus.
My article "A New Investigation of the 'Mystery Letters' of the Quran," asserts that the letters preserve an early attempt to document the textual sources used to compile the Quran. (If you'd like to read it, you can download it from my Academia.edu page.)
My propsed solution to the controversy should be unacceptable to Muslims, who believe the Mystery Letters are part of the divinely revealed text of the Quran. I've produced a scholarly work that contradicts a theological reception of the Quran. Even so, I've never received any complaint from a Muslim about my article and I've observed that my article is cited and quoted in scholarly books and articles about the Quran written by Muslims. They don't have to agree with me. But they've never dismissed me as being out of line to publish on the topic, such as Dr. Aslan has experienced.
Now, Dr. Aslan states that if all we knew about Jesus was that he was crucified, we could conclude that he was a "zealot" or a "revolutionary" viewed as dangerous to the State. He asserts that crucifixion was reserved only to insurrectionists such as the survivors of Spartacus' revolt.
The texts of the Gospel do make it very clear that Jesus was crucified because of Roman concerns that he made claims to authority over that of Rome. But the assertion that crucifixion was only used for revolutionaries is a bit of an overreach. The story of the "Widow of Ephesus" in Petronius' Satyricon (111.5) describes latrones being crucified. Like the Spanish ladron, this simply means a thief or robber, not an insurrectionist.
But I disagree with his claim because I can cite a counter text from a primary source. I don't dismiss his claim because he's a Muslim. Sadly, Dr. Aslan is forced to argue past a barrage of ad hominem attacks before he can even begin to speak on the area of his expertise. You comported yourself with dignity in that interview, sir. Good luck in your continued scholarly pursuits.