In my personal experience, and in 25+ years driving the route to Big Bear (both highway 330 and 18), when there is a chain check and when stopped by the CHP, I have almost always been asked if I'm carry chains. Sometimes a simple Yes will get me through, but there have been times when they ask to see them.
If they ask and you can't show them chains, they will turn you around. In a previous 4x4 truck, I simply carried a bag with chains that wouldn't even fit the tires; just for something to show if asked. With the LR4 I carry a set of SCC - Z Chains that will work if needed. I've had to present them but never had to put them on driving the mountain. In my opinion, $95 was cheap insurance from either getting turned around and driving home or finding a local hotel until the chain check was lifted.
One final note, with the snow we have been getting lately in SO CAL, so far this year I've only seen the chain requirement for everyone but 4x4 vehicles with snow tires. There are times after much bigger storms and snowfall totals, I've seen where they require chains on ALL vehicles including 4x4's. So good to be ready when that happens.