This is somewhat tricky to answer because brigandines actually have 3 layers. There is the metal plates, and the outer covering. These are the obvious parts - the metal plates protect the wearer (they're really the point of a brigandine, after all), while the outer covering determines its appearance and is what is referred to in many contemporary documents. For instance, accounts will refer to brigandines covered in blue velvet. However, this isn't all - there's also the middle layer, the thick cloth backing. This is what actually holds the garment together. This layered construction is visible in this example in Basel. Here almost all of the outer covering (originally red silk) has been lost, leaving the tinned plates and the canvas backing.

This three layered construction is important because there -are- leather-covered brigandines. The best preserved and documented one is in les Invalides in Paris. Since the catalog of Les Invalides is not online, and their entries for the collection are spotty, it is impossible to tell from the image whether there is an inner layer of cloth behind the leather (as there were with fabric covered brigandines). Canvas is much less prone to stretching than leather, and so it would make sense to make canvas the actual base of the brigandine, even if you were covering it with leather. In this case, a brigandine would be leather-covered but leather would not be the 'base garment' for the brigandine. Looking through the secondary literature, rich fabrics are more commonly mentioned in accounts than leather, though perhaps velvet brigandines warrant more comment than those covered in leather.