If you've recently separated from Intel and have some medical appointments/procedures pending, you may want to contact Intel Health to get your COBRA coverage status expedited ... 877-466-9236. Note that even with the status being expedited it may still take 1-2 weeks for the insurance companies to get their records updated.
I had a dental appointment and and some lab work that had to be pushed out by several weeks since both providers said my insurance was cancelled as of May 31st. I was told that I could still keep the appointments, pay for the services and then submit to get reimbursed but I chose not to.