DRUMMER CAFE

Without even looking I can bet that the stickings noted are what's recommended for "What's best" or "easiest" to move around the kit (so your hands don't cross unnecessarily, etc.).

That said, if it is EASIEST for YOU to play the entire thing with only ONE hand, or your feet, or a stick in your teeth, then that's what you need to do.

99.9% of your drumset drumming life will be spent playing sticking that are comfortable for YOU.

With all THAT being said, you should likely heed stickings if noted.

In general, if the sticking is not given, work it both ways.  You don't want to stick with just what is comfortable.  You want to develop the coordination and independence to play with either left leading or right leading.  When moving through the kit on fills, there will often be one sticking that works most efficiently, e.g., avoiding crossing your hands.  BUT, working on crossing your hands or using different sticking is good practice.  There are indepence and sticking excersises that will help you in many good books available and referenced in other posts.

Enjoy!!