Arabic, Indian, Thai, and Chinese artists observed elephants first-hand and created paintings reflecting them. How likely was it that European artists needed to base a painting on only a description by western travelers? Did trade caravans/explorers carry artwork across Europe/Asia?
Did trade caravans/explorers carry artwork across Europe/Asia?
Actually, they carried animals!
In addition to mundane uses for mundane tasks (the camel is the 18-wheeler of the medieval Islamic world), "exotic", fierce, and unusually striking animals played two key roles in international medieval political culture. First, the keeping of a royal (or sometimes even princely) menagerie was a key display of power--having the connections to obtain and the wealth to maintain the animals. Second, the gifting of animals was a major diplomatic strategy--to mark formal diplomatic relations, to assert "Hey, I'm here and powerful." This is an international and even intercontinental medieval phenomenon: thus a giraffe makes it from the interior of Swahili Africa to India, whence it travels to imperial China and is understood as--painted in the manner of--a unicorn. The courts of medieval Europe were part of this trend, absolutely. Perhaps the most famous menageries are in London (where in the 13C, the polar bear would go swimming for fish in the Thames) and in the Norman Sicilian court; the most famous elephant is undoubtedly Harun al-Rashid's gift to Charlemagne.
But would most manuscript illuminators have seen an elephant in person? That's more doubtful. When we look at European illustrations of elephants, we see a range from the realistic to the plausible to the nice try there.
Bestiaries had a bit of physical description, but were more concerned with talking about the animals' behavior as moral lessons for humans (elephants are the natural enemy of the dragon; they are a good example to people because they are extremely loyal and mate for life). Most likely, artists who had not seen an elephant in person and could work from memory--which would have been the vast majority of them--were copying earlier illuminations. Medieval artistic tradition was heavily iconographical, that is, drawing in types.
Corollary: Today Ganesh (an elephant-headed Hindu deity) is represented in a wide variety of art for Indian homes. Would representations of Ganesh have been relatively as popular and geographically as widespread a few centuries ago?