You need to deal with someone much higher up the totem pole with he insurance company to get a right answer and simply cancel your insurance. I don't know why you would need to wait until 30 days prior to expiration of the policy, as that makes no sense. Normally, if you don't cancel a certain number of days before the policy ends the policy will automatically renew and you don't want that.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.
The answer is likely within your insurance policy or contract. Often the policy can only be canceled based on specific life events and cancellation can only occur within a certain period of time before the life event. That would certainly make sense within the information the insurer's service associates are providing. Take a look at your policy or contract and see what it says about terminating or cancelling your policy. That document governs your insurance coverage.
I would sit down and write a letter notifying the insurance carrier of your cancellation, effective immediately. I would send this letter, via certified mail, to the place where the policy identifies as the address of the carrier. Make a copy of the letter, the certified mail receipt when you send it, and then a copy of the return when you get it back from the postal service. Most health insurance policies can be cancelled at any time.
The response provided to your inquiry on Avvo.com in no way creates an attorney-client relationship regarding the issues discussed in this forum. The advice offered is informational only and is not held out as accurate interpretation of the unique issues in your case.