"She said Cigna does not directly benefit from such savings."

The quote indicates that the employer group was self-insured, and Cigna was the plan administrator. This means that Cigna is not insuring the health plan. Cigna is probably paid a per member per month (PMPM) fee for third party administration (TPA). The actual medical claims and associated costs are directly paid by the self-insured entity (the employer group).

Self-insurance can make actuarial sense for companies with >2,000 employees.