There are a few varieties of recluse spiders in California. We may not have brown, but other than experts, who would know the difference? If you can tell one recluse spider from another, you're an expert to me. The others are poisonous too.
The range of animals is always tricky. You'll have experts insisting a particular creature isn't in a specific place, but the range of the creatures changes over time.
For example they tell us we don't have hobo spiders in California. I'm sure it was true at one time. It may be true still. But it likely won't be true in the future.
Read Vetter's book. Brown Recluses live in something like large colonies. A few houses may be infested, and neighboring homes may be free of them. Vetter describes a family in KS that lived in a house with 2000-something Brown Recluses. They have basements back there. One possible bite occurred in 10 years. A house is a good habitat for them. Within their range, they are not hard to find, they aren't rare. Tip over a board and find a few. Schoolboys can catch them by the dozens. We would know if they were here. There have been a couple of dozen specimens since the 1930's found in the LA area and Angeleno's aren't finding them.You can send a photo of a dead spider to UC Davis or UC Riverside if you think it's a Brown Recluse. It isn't. I moved my family in a UHaul van from Missouri to LA once, that's what Okies do. We might have had a few in the boxes or something. Couple of dozen specimens, 20 million people, 85 years, they just aren't reproducing down there.
This isn't what the desert recluse does either. It doesn't live in houses in large numbers. If you find someone who stuck his hand under a rock at Willow Springs and took a bite, then developed typical creeping necrosis, you might convince but you won't impress. These are vanishingly rare events.
Same thing in Florida, much more similar to their native habitat than CA. Hundreds of Brown Recluse bites reported, but almost no spiders found. Just because there's a bad ass spider in Arkansas doesn't mean it can find it's favorite prey and outcompete local spiders in CA or FL.
I have a confession. Doctors sometimes make shit up. When you see your doctor with a skin thing and they tell you it's a Brown Recluse bite, they don't know what it is. They almost certainly never practiced where BR's live, never saw a bite, never saw the spider and might as well tell you it's a whale bite because they never saw that either.