Not every deity need supply power to their followers through a specific form of divine magic and there's really no need to be cookie-cutter about the approach. Instead of Priestly spells, some deities may instead provide knowledge, guidance, natural assistance, or mystical power. Thus, just as there are multiple branches of arcane lore (wizard, bard, cipher, alchemy), there can be different branches of divine inspiration (priests, druid, monk, philosophy).
The deities don't provide any power to anyone, as far as I can tell. As it says in the link, "Such men and women have found a divine link to their chosen deity, but their abilities stem solely from within." It sounds to me like you're saying that priests don't all have to be exactly alike, nor does any other class. If that's the case, then I completely agree, and I didn't mean to suggest otherwise.
The thing is, every class gets its abilities from the power of their soul (or in some cases, other people's souls). Each class uses a different method to access this power. Priests use their faith, wizards use their knowledge and research, chanters use the power of storytelling to convince ambient spirit energy to help them out, etc. Since monks are a separate class from priests, I don't think they should use the same method to get their powers.