But you are urban. You are near a major city, and adjacent another small one like you said. Urban versus rural is not a measure of closeness to nature, it's a measure of closeness to other humans.
Kinda crazy to see the entire I-5 length between San Francisco and Los Angeles classified as "metro". Perhaps the metric they're using doesn't work so well when counties (which is what they classify) are so large, and they primarily care that some city of over 50k people exists in it "somewhere". Some of those counties appear to be as large as or larger than some of the smaller states in the Northeast.
As you suggest, a lot of what is classified as urban is not urban especially by the standards of someone who barely considers the South Bay as urban.
Certainly I can normally go into town for an evening of theater but most people would consider my house to be in an urban setting.