Referrals from Kaiser to New Providers

I recently switched from my parents’ Kaiser Permanente (KP) plan to a Cigna plan through my job and am in the process of finding a new rheumatologist. According to the Cigna plan website I do not need a referral or PCP to get an appointment with a specialist. However, the major hospital I would like to go to for treatment does require a referral. I was told it’s so they can triage me based on my condition and then match me with an appropriate physician and appointment date. Last month I reached out to my KP doctor and had them send over what I thought was a referral. Last week the new doctor’s office said what was sent by KP was insufficient and to talk to the KP doctor again because they needed records included.

Today when I called the KP office the nurse told me that they can only send letters of introduction and not referrals as a referral indicates that they’ll “pay for your consultation”. What does a referral have to do billing between provider’s offices? I was under the assumption that a referral is a statement detailing my condition and treatments and how it is medically necessary for me to be seen by another provider in a different specialty rather than any any promise of payment.

The nurse also said that she would include visit notes from my last few appointments when she resends the letter of introduction. Does this sound sufficient? Is there a different way I should go about transferring care from KP?