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I have horrible obsessive-compulsive tendencies to reword any phrasing that I find could sound even slightly better. In my time I've learned that trying to fight it is entirely pointless and will never end up working.
"access to rain boosted STAB moves" implies that it has access to rain boosted moves, with STAB being secondary. However, access to rain boosted moves simply means that it has Water-type coverage, and isn't necessarily the main point that's meant to be conveyed. To say that its STAB moves are further boosted by rain helps clarify this ever so slightly.