That's very true of the setting.
The system of magic, however, doesn't really have much synergy with the setting material. For the most part, the system of magic in L5R 4e could easily be used for any magic in any setting with just a new paint job and almost no modification under the hood. There's nothing really there to distinguish Rokugani "magic as an extension of a kami-based religion" from POWS (plain olde wizzard spells) magic. Flinging spells as a Shugenja in the L5R RPG doesn't really feel that much different from a spell-caster in any other system/setting combo.
Oh come on... Then a Lion Deathseeker is an awesome berserker that every Lion wants to be because of their power on the battlefield? Nope, because it's a dishonored Lion wanting to regain his honor or dying doing so...
Also, you say there's nothing that shows system-wise the fact that they are based on kami? How about the universal spells that you have even before selecting your spells? Commune, Sense and Summon. These three spells are directly in this direction. Also, the fact that you have to roll a Ring instead of a trait shows that have to work with your spiritual connectivity with kamis of this elements.
Are you suggesting that they should remove "Spellcasting Skill" and use "Theology skill" instead? Will that make a difference? A priest doesn't mean it should be a frail healer, heck look at the Kuni Shugenja, they are far from being a frail healer and they aren't afrain to throw everything they have, even themselves, against an Oni. I really wonder what is your definition of "Priest" because if your definition is really "A frail healer praying to god" then change it, because that's not the definition of a Shugenja...