ody My last day of work at my former employer was 5/13/2014.

I signed up for COBRA.The COBRA provider has told me that because coverage under my old employer ended on 6/10/14 and their COBRA coverage does not begin until 7/1/2014, I will not be reimbursed for any expenses between 6/10/14 and 7/01/2014. Is this correct? The human resource specialist at my old job told me that COBRA is designed to make sure that employees DON’T have gaps in coverage.