As an Iditarod runner Mr. Paulsen must know something about survival. However, if he is to write about survival he probably should know that any attempt to strike sparks from a knife or hatchet is very unlikely to succeed. A proper "fire steel" is tempered very hard, about as hard as carbon steel can be made, something like a file bade for cutting other steel. Such a hard steel would be entirely unsuitable for use in a knife or hatchet as it would easily chip and shatter on impact. The temper of steels for knife and chopping implements must be drawn down to a softer and more resilient steel, more like a spring than a file, and as such would be too soft to strike sparks with a flint. Furthermore, in the past 50 years most knives and small camp axes such as Mr. Paulsen describes have been made of stainless steel. It is not possible to strike a spark from stainless no matter how it may be tempered.
I have not read this description of how Mr Paulsen started a fire. However as we are talking in this discussion about he kind of materials that are needed to start a fire, I would like to point out that ancient people started fire by rubbing wood together. As a matter of fact in India people still start fires for some religious ceremonies using this method. IN this method a pointed piece of wood stick is pressed on to a wood block and simultaneously rotated at fairly high speed by means of movements of a thin rope looped around the stick. This results in a small cavity being created in the wood block, which becomes very hot. Some wood powder (like saw dust) is added quickly to this cavity. This results in the wood powder is catching fire. This fire minuscule fire is escalated in to bigger and easily sustainable fire by carefully adding dry grass and then thin twigs to it.
Exactly and a good point to mention because that is basically the only way the boy could have made fire in that situation. With just a little basic know-how and a lot of trial and error experimentation he could have constructed a "fire drill" which produces glowing embers from the heat of friction. We've all seen movies in which a person produces fire by twirling a stick between their hands and it can be done that way but it is much more easily done if the stick is spun with a bow drill.
Using a bow drill as a fire drill also eliminates the need for something to catch the sparks of flint and steel. I compete in events at Mountainman Rendezvous where fire making is part of the contest. One needs the proper medium to catch the sparks. Bits of charred cloth are the standard medium used to catch sparks. Nothing else I have ever heard of will substitute for "char-cloth" to catch and hold a spark. One first strikes sparks from the fire steel onto the char-cloth where they glow and grow. The I can produce a visible flame in less than thirty seconds but some really expert individuals have done it in less than 5 seconds. But a proper fire steel, sharp flint, char-cloth and fine dry kindling are absolutely essential, you'll never make fire by striking sparks directly into the kindling, no matter how finely it is shredded.
It might be just as hard as rubbing two sticks together and hoping that not just a spark but some fire erupts from it. I have seen it so many times in media, but it hasn't happened when we go camping.