For most insurers this is true, the umbrella only extends the liability cap on underlying policies an/or plugs any coverage gaps that may occur in the underlying policy(ies).
In the US there are a couple of insurers (RLI, USLI) that will write a personal liability policy with no requirement for an underlying policy. They do have requirements, including minimum coverage amounts, if you do have homeowners/boat/etc. policies. If you have none of the above then their insurance
covers you down to zero, but if you do own a home then it covers like a traditional umbrella. Costs more, but if that's what you need...
Do you really have zero physical assets (home, boat
, car) that require liability insurance
, and yet have enough other assets that you need liability insurance protection? Just having car or boat
liability insurance is usually enough to get an umbrella.