Read the terms of your umbrella policy. All of them have minimum coverage requirements for your primary policy. They aren't going to beat them at their game.
Example:
Geico: GEICO requires a minimum bodily injury limit of $300,000/$300,000 and a property damage limit of $100,000 or $250,000/$500,000 and a property damage limit of $100,000 on your auto policy to qualify for an umbrella policy. Homeowners/Renters Personal Liability coverage of $300,000 is also required. Contact us to receive a quote for increased auto insurance limits.