Subject-verb agreement: The clause counts

A reader found fault with this sentence from a front-page story Sunday: 

The number of households in the state that depend on food stamps has increased 45 percent over the last two years. 

She thought the writer and editors had made an error in subject-verb agreement. "... the verb should be 'depends' to agree with the the subject, 'number,' not 'households,' which is the object of the preposition, 'of.'" But the verb that needs to agree with "number" is "has increased." The relative clause "that depend on food stamps" does refer to "households."  

The reader recommended that N&O writers buy a copy of "Harbrace College Handbook" to help them with their grammar. Indeed, this little handbook (1977 edition) helped me write this post. I was able to use the sections on subordinate clauses and collective nouns to show that this sentence is correct as written.

I also reviewed some rules of diagramming to come up with this partial diagram of the sentence. Please pardon my weak penmanship. The subordinate clause is indicated by a dashed line from the noun it modifies to the clause.