Here's the deal on homeowner and personal umbrella insurance:
Long story short: you MUST read your policy forms. In detail. There's no way to know for sure if coverage exists for this scenario unless you read the form. For the homeowner policy (with attached Personal Liability, which is the coverage in question), you'll look under Section II and pay close attention to the exclusions section.
If you called up your agent and asked the question and he gave you an immediate response of "yeah it's covered," I'd consider him a liar until I read the policy myself, or he directed me to the applicable sections in the policy language.
Insurance companies sometimes use a pure ISO form, sometimes emulate the ISO form with their own changes, and sometimes create a fully proprietary policy form. And there are multiple versions of the ISO forms. I can tell you with certainty that the 2000 version of the ISO homeowner form has an unambiguous aviation exclusion:
B. In addition, certain words and phrases are defined as follows:
1. "Aircraft Liability", "Hovercraft Liability", "Motor Vehicle Liability" and "Watercraft Liability", subject to the provisions in b. below, mean the following:
a. Liability for "bodily injury" or "property damage" arising out of the:
(1) Ownership of such vehicle or craft by an "insured";
(2) Maintenance, occupancy, operation, use, loading or unloading of such vehicle or craft by any person;
(3) Entrustment of such vehicle or craft by an "insured" to any person;
(4) Failure to supervise or negligent supervision of any person involving such vehicle or craft by an "insured"; or
(5) Vicarious liability, whether or not imposed by law, for the actions of a child or minor involving such vehicle or craft.
b. For the purpose of this definition:
(1) Aircraft means any contrivance used or designed for flight except model or hobby aircraft not used or designed to carry people or cargo;
Whether or not your homeowner policy uses that language is unclear until you review the policy. Here's the older ISO 1991 language, which is more ambiguous but it could still be argued that there's no coverage:
h. Arising out of:
(1) The ownership, maintenance, use, loading
or unloading of an aircraft;
(2) The entrustment by an "insured" of an
aircraft to any person; or
(3) Vicarious liability, whether or not statutorily
imposed, for the actions of a child or minor
using an aircraft.
An aircraft means any contrivance used or
designed for flight, except model or hobby
aircraft not used or designed to carry people
or cargo;
If you have a "rider" on your homeowner policy that increases the Personal Liability to $1MM, then it's a near certainty that it uses the same language as the policy.
If by "rider" you actually mean a personal umbrella policy, then it's a little more tricky. The umbrella may use be a "follow form" and use the exlusionary language of the underlying policy. Or it could be a true umbrella, in which case you'd need to read the umbrella policy language to determine whether there's coverage. The aviation exclusions on umbrella policies are nearly identical to the language in the homeowner policies. [EDIT] - Even if you managed to determine that there was coverage on a "true umbrella," if you didn't also have coverage in the underlying homeowner policy, you'd still have a large gap in coverage before the umbrella policy would respond; likely at least $300k out of pocket.
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All that being said, it's within the realm of possibility, though improbable, that you have no aviation exclusionary language in your policies. But I'd bet you a beer that's not the case.