You were refused. Read the subsection again.
A county assessor who denies an exemption must notify you. You may then file an assessment appeal with your county Assessment Appeals Board — the window runs from July 2 to September 15 in most counties, and to November 30 in some.
Cal. Rev. & Tax. Code §205.5(b); §1603 (appeals)
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Your appeal route
File an assessment appeal with your county Assessment Appeals Board. The window opens on July 2 and closes on September 15 in most counties, though some run to November 30 — check yours, because it is one of the few things that does vary by county here.
California does not prescribe what a denial notice must contain the way some states do, so there is no "the letter is defective on its face" argument to make here. What California gives you instead is a clear four-part statutory test and an appeals board — and in most refusals the statute's own words are the answer.
One more thing worth checking
The most common wrong refusal in California is of a veteran whose combined rating is below 100% but who is compensated at the 100% rate through individual unemployability. §205.5(b) names unemployability as a qualifying condition in its own right, alongside a 100% rating. Ask the assessor to read subsection (b).
Read the record on §205.5