In this case it probably doesn't matter .. the odds against Mix having said coverage is greater than the Pentafecta odds of the Kentuck Derby .. (183,000:1 this year if one didn't know)The notion that you must have a contract for your liability insurance to cover you is false. While it may say that in your policy - it is essentially meaningless because the mere act of promoting and conducting a business is itself a contract with the public at large. A court would not allow an insurer to escape coverage on such a flimsy technicality. Liability is often irrespective of whether the claimant was an actual customer or even connected with any customer you have. Most claims will have nothing to do with your contract or anyone with any kind of relationship to your business.
The cheap online DJ insurance is being sold sight unseen to a lot of people who's activity does not rise to the level of a commercial business and therefore is vulnerable to a lot of fraud. With no other evidence of any business activity the contract may be necessary to show that you are not simply filing a fraudulent claim (especially around property theft, etc.) When these policies first became available the most common claim was fraudulent equipment loss.
However, if you have a claim resulting from an event and long time client you have been servicing for years - the lack of a written contract would not likley be enforceable as a denial of the claim. This is especially true if you pull an Accord certificate for the event, which as proof of insurance is an affirmation of coverage by the insurer.