Not quite, but sort of. Umbrella carriers typically require you to carry a certain amount of liability insurance on your auto and home policies before they will sell you an umbrella policy. For example, a requirement might be at least $300k in liability on your homeowners, and 250/500/100 on your auto policy. So while you can't have state minimum and buy an umbrella policy, you don't necessarily have to have the highest amount of liability coverage offered on your homeowners/auto polices to be eligible to buy an umbrella policy.

Also, your umbrella policy can be from any insurer that offers one. It does not have to be the same insurer that you have your home or cars with. In fact, depending upon who you have home/cars with, your carrier may not even sell an umbrella policy.

EDIT: I just played around with the RLI website, and they even offer an umbrella if you carry 100/300/50 on your cars. Premium is a little higher than if you carry higher limits on your cars. With the 250/500/250 limits I carry, I could get a $1mil umbrella for $469/year. Mind you, I have an 18 year old driver, which will affect any premiums at all related to auto insurance/umbrella insurance.