If Bozo the Clown was trying to prove the Qur'an scientifically accurate, do you think it would be problematic to doubt him?
It's not disbelief. It's not the Qur'an you're doubting, it's the person's claims about the Qur'an. In fact, the Qur'an encourages Muslims to investigate in these circumstances:
O you who have believed, if there comes to you a disobedient one with information, investigate, lest you harm a people out of ignorance and become, over what you have done, regretful. -- Qur'an 49:6
Islam Q&A goes into much detail on this topic, writing verifying news is required according to sharee’ah. So, if you go by this ruling, not only is it not disbelief, it's not even haram; it's obligatory.
Also, we don't simply slip up and end up a disbeliever; it needs to be done intentionally. In the Open Letter to Al-Baghdadi, a large number of scholars worldwide endorsed a document in response to ISIS leader Al-Baghdadi's behavior; they write:
... disbelief requires the intention of disbelief, and not just absentminded words or deeds
Some other fatawa that repeat the idea that disbelief requires intention: MuftiSays, Islam Q&A (1; 2; 3; 4), IslamWeb