Let's keep in mind that Tolkien was drawing on a much older mode of narrative art than 20th or even 19th century literature. In the classical and Germanic and medieval legends which formed most of Tolkien's leaf-mould, false modesty (or any modesty) was not a component of the heroic character: Achilles and Sigurd and Beowulf and Gawaine are quite open and proud about their own rank and badassery.