Like everything else, most tax matters are on the honor system. If the payment is not reported, you would only get caught if audited -- but if you are audited, the IRS will look at all your business transactions and you will have to prove the income is NOT taxable, not the other way around. (With the IRS, you are guilty unless you can prove yourself innocent.)
Insurance payments for damaged or stolen equipment are taxable if they are more than your cost basis, taking depreciation into account. For example, suppose you bought a commercial oven for $5000 5 years ago and you have taken $3000 of depreciation on it. You lose it in a fire and your insurance pays replacement value of a new oven ($6,000). The taxable amount is $4000, the difference between the payment and the residual value after depreciation ($2000). On the other hand, if the insurance only pays present fair market value for used equipment (let's say $1500), then you have a casualty loss of $500.