No. It's probably not. Companies the size of Disney don't carry liability insurance. They are the liability insurance.
I do confess that I'd love to own the company with the financial fortitude to underwrite their policy though.
Disney and companies like it do usually carry liability insurance. What you typically see with such companies is layered insurance: (a) the primary layer is a "fronting" insurance policy, under which the insured gets an insurer that defends and pays the claims until primary liability limits are exhausted and the premium paid essentially ends up equaling all the defense and indemnity costs covered by the insurer plus a premium added for the insurer's services; (b) a first layer "umbrella" policy for a fairly high premium that typically provides, at its excess level, both defense and indemnity for the same type of claims that would be covered by the terms of the primary insurance, and also covers at a primary level a class of claims that are not typically covered by primary insurers; the insurer is usually responsible for the costs of defense and indemnity, but there may be deductibles, particularly for those types of claims not typically covered by the primary policy: (c) numerous layers of excess insurance over the umbrella policy, which often provide coverage for liability but not defense, and, stacked on top of each other, often provide tens of millions, to even hundreds of millions, of total liability coverage.
Sometimes there is self-insurance at the primary level and the umbrella and excess levels are above that, but that is not the usual arrangement both because there are many umbrella and excess insurers who will not provide insurance unless they know there is an experienced primary insurer in place, and because insureds do not want to have to handle their own liability claims, including having to hire and constantly supervise defense lawyers across the nation, i.e., primary liability insurers are in the business of doing that and can provide that service often for less than it would cost if the insured handled its own claims.
With the pandemic, there can also be an issue as to whether insurance applies at all to the personal injury claims. Many policies exclude coverage for pandemics unless the insured pays for a rider to the policy to cover it. Moreover, future insurers likely will exclude any claims arising out of the current pandemic. Nevertheless, existing insurers, even if they do not cover the claims, still communicate with the insureds about them, including providing advice like for the insured to add a disclaimer/assumption of risk advisory when it reopens.