Your business liability policy covers you for claims due to your negligence. Medical payments coverage provides payment for bodily injury to third parties that occur on the premises you own or rent as a result of your operations regardless of negligence.
The rationale for this coverage is insurers believe an injured party is less likely to sue you if they receive prompt payment for their medical expenses. Medical payments coverage expedites payment to an injured party without their having to sue.
A relatively high medical payments limit chosen by you might reduce the chances of a minor claim escalating into a lengthy and expensive claims process.
For claims that might be larger than your chosen medical payments limit, the liability portion of your policy would apply if it were determined that you were negligent. Regardless of your fault the commercial liability policy will provide a defense if you are sued by a third party, even if the claim is groundless.