He says that he cannot drink fermented wheat or grape. Another character says that it is okay, because mead is from honey. Ahmad ibn Fadlan then proceeds to drink it.
Is this Hollywood history or is there some basis to the misconception about the Islamic prohibition on alcohol?
This has actually been a longrunning debate in schools of Islamic jurisprudence over what qualifies as khamr (intoxicant, plural khumur), which is explicitly forbidden by both God in the Qur'an and the Prophet Mohammed in the Hadith.
On one side were the Maliki and Shafi schools, with their roots in Arabia, which advocate the belief that all alcoholic beverages are khumur and are therefore forbidden. This goes back to the days of the Maliki school's founder, Malik ibn Anas, who cited scriptural evidence for general prohibition based on the Qur'an and Hadith. Later Maliki scholars like Sanhun would say that the prohibition applies to drinks with even the capacity to ferment, though later scholars abandoned this view. Similarly, the founding Shafi scholar Idris al-Shafi argued for general prohibition based on the traditions of early Islamic communities. Later Shafi scholars like al-Mawardi, al-Baghawi, and al-Rafi'i focus largely on using their claims to counter the Hanafi stance.
On the other side was the Hanafi school, with its roots in Iraq, which argued that only alcoholic beverages explicitly mentioned in the Qur'an and the Hadith (grape & date wine) are forbidden. They also claim that that it is not drinking per se that is the sin, but drunkenness, citing verses such as one from the Hadith where Muhammad condemned the "last cup which intoxicates." This narrow prohibition started with the school's founder, Abu Hanifa, based on his literal interpretation of Quranic verses on khamr. Much of the debates within the Hanafi ask whether it only applies to only grape & date wines, all grape & date juice drinks, or only certain methods of production or fermentation. Starting in the 12th century with scholars like al-Marghinani, Hanafi scholars began declaring broader and broader categories of alcohol unlawful. By the 14th century, the belief in general prohibition of alcohol was commonly accepted, and works of earlier Hanafi founders were reinterpreted to keep things ideologically consistent.
Why did the former stance eventually win out over the latter? As the 12th century Maliki scholar Ibn Rushd (better known in the west as Averroes) points out in his treatise Bidayat al-Mujtahid, the Hanafi school has a weaker legal basis. There's essentially a hierarchy of precedence when it comes for determining Islamic law: explicit commands in the Qur'an > explicit commands in the Hadith > qiyas (analogical reasoning) to determine implicit laws in scripture > ijma (scholarly consensus). And the schools in favor of general prohibition (especially the Malikis) built a far stronger case based on scripture than the Hanafis. There were also likely social stigmas at work, with consumption of alcohol becoming increasingly associated with pre-Islamic or foreign societies, and the Hanafis increasingly seemed like the odd ones out.
Since ibn Fadlan served in the Abbasid court at Baghdad, where the Hanafi school was flourishing in the 10th century, it's perfectly reasonable for him to hold such a stance.
My main source was "Contesting Intoxication: Early Juristic Debates over the Lawfulness of Alcoholic Beverages" by Najam Haider in Islamic Law & Society (which can be read here, with some supplementary info from John Esposito's book Islam: the Straight Path.
Your post raised another, tangentially-related question: was wheat beer the only kind of beer back then? Did they not make it from barley until later? Or in this case does "wheat" just mean "grain"?