Here's the thing ... while WE deal with things such as interpreters and related policy often - many doctor's offices do not.
The person may honestly not know what the proper way to handle interpreter booking IS and is making the assumption that "if YOU the Hoh/Deaf person needs them, then it should be you that books them".
Keep in mind that this person may have never booked an interpreter before - and truly honestly doesn't know. They're thinking things like you (the Hoh/d/Deaf person) know what you need, who to call, how to "book them", how to make sure it's the "right type of interpreter" etc... and they (receptionist) might "mess up" and not know how to get the right person etc.
I've found it's VERY helpful to explain the process briefly to the receptionist etc, and also have a 'contact person' at the interpreter agency who the receptionist can phone to walk her/him through whole process correctly and explain how payments etc are made, who's "Responsible for payment" how that all works etc.
(***You are NOT getting involved in the booking of an interpreter - simply giving the Dr. office receptionist a "contact" who can help the Dr office book the interpreter***)
While it may not be your "JOB" to do all this extra work ... taking the time now to
politely, patiently, and kindly help inform and educate this person/dr. office how to properly handle the request for an ASL interpreter WILL make things SO much easier for you - and any other Hoh/Deaf person in the future.
Taking the time to explain this properly, and put them in touch with an agency with RID etc certified interpreters also helps ensure that they will USE proper licensed and certified interpreters instead of "cutting corners" because they don't know better etc.
I'd contact the agency/ agencies listed, and then ask to speak to someone there who is able to walk a medical office through how booking an interpreter works etc. Ask the agency person (lets call them "Sue") if there is a direct line the Dr office receptionist could call, or an email they could use to get them in contact with "Sue" directly since she's already aware of the situation and what information that the Dr. office will need to know about etc. ("Sue" can also see if the Dr. Office already has an account etc with "Sue's" agency so she can let the Dr. office know that when they call as well)
Most people - even those who "should" - simply do not understand the way booking ASL interpreters "works", who "funds" the ASL interpreters, what the legal requirements are etc.
As people who DO understand how to book interpreters and how critical it that the interpreters be licensed, certified etc. we DO have an ability and obligation to help people, (especially those in places like Drs offices) understand the "system"
Hope that helps.