You really do. Because the operator will usually be held liable for any bodily injury claim. Even if he uses an independent contractor, he can still be held liable.
The greatest exposure is a contractor's employee getting hurt, collecting Workers' Compensation, and then suing the operator because he "failed to furnish a safe place to work." The Commercial General Liability (CGL) and Umbrella Liability policies usually cover these claims, but if you have frequent claims, your premiums will increase. Continuing to have them may make you uninsurable. And, if you have a large Self-Insured Retention, you are paying directly for these claims.
Establish in a Master Service Agreement (MSA) who is responsible for each loss and ensure the other party has the correct insurance to back up its responsibilities.
The first three areas ensure the contract works correctly. The fourth area ensures the insurance meets the specifications, requiring more knowledge than is shown on a standard certificate.