I don't think that is quite right. I had a book about computer graphics using OpenGL from before then, and I remember it saying (something like) that various polygons were supported at the API layer, but the GL implementation would decompose them into triangles at some point, and this could have surprising results for texture mapping, so it was typically a good idea to triangulate shapes explicitly.

One major technical reason that triangles are nice is that every triangle determines a plane, and rendering points onto a bitmap is easier if you know the surface is planar.