Honestly, I'd rescind any permission for them to talk DIRECTLY to your physician.
The reason is that YOU need to have a seat at the table any time your physician is involved. S/He's not the SCHOOL's physician-- s/he's your child's physician.
Think of a good 504 plan as being a STOOL. There are basically three legs (sometimes four) to a solid 504 plan. By 'legs' here I mean input streams of expertise.
a) MEDICAL-- this is where your physician comes into things(and to a lesser extent, a school nurse... and yes, I DO mean 'lesser' extent, because this is about medical diagnosis and practicing within one's professional scope of expertise. Nurses are not allergists.) The medical stream is the one offering advice on how much exposure is "okay" or not, what kind of responose is appropriate under which conditions (ie-- for a non-specific symptom of asthma, does this child get epinephrine? Or an inhaler?)
b) DAILY REAL-WORLD MANAGEMENT AND RISK ASSESSMENT/RESEARCH-- this is us. Allergists are medical experts, but they are NOT the experts at navigating the world with a particular child and keeping him/her out of anaphylaxis. WE ARE.
c) SCHOOL OPERATIONS-- this is school staff. They know layout, they know logistics of first-response, they know their staffers, they know the culture of the school community.
d) (possible) Special Education needs-- can be GT/SpEd needs, but this will have to dance with the other three.
Every one of those voices needs to know what is being communicated between the others during this process. Schools have an unfortunate tendency to cut parents out of the loop once they have access to the doctor, and they often agree (between the two of them) to things that PARENTS, being experts in daily tactical management, would KNOW cannot work. Oh, sure, they may be fine in "theory" but we as parents know when we've got a child that can't really be relied upon to, say... resist food trading. Or to speak up assertively when not feeling well. Some kids can handle some situations better than others. Most of the time, allergists don't have a great handle on a child's relative sensitivity, either-- unless parents have told them about reactions, that is. What is fine for one PA child (eating M&M's and bakery cupcakes) might be really, really dangerous for another child, even though both are patients of the same allergist. KWIM?
That is why parents ARE experts who must have a place at the table when a plan is being discussed.
Secondarily, who is compensating the physician for his/her TIME in all this phone and fax and e-mail time with the school, hmmm? Is it the school? You? Not cool-- s/he's YOUR physician, and needs to be acting in his/her PATIENT's best interests.
Honestly, I'd rescind the permission. I'd just explain that you have privacy concerns re: turning over that kind of access, and you are also concerned about the possibility of "confusion" during a reaction-- you DO NOT want the school to be calling your physician during a reaction. Say it with a smile, and make it clear that you are HAPPY for them to have access to your physician-- but that ALL access needs to be in writing and go through you.