I think this is a very important topic that has potential to backfire, depending on the situation. There are a few things to consider about asking your PD or program chair to call other programs on your behalf.
#1- To your home program, this could come across as you being uninterested in your home program. With some programs, this could even result in you being ranked lower on their rank list. This is more likely to occur if your home program is small, low-mid tier, and values loyalty over qualifications (probably not the kind of program where you want to match anyways!). However, if there are multiple derm applicants from your class who are applying, your PD/Chair is a reasonable individual, and you attend a high tier med school then I think asking for networking on your behalf is fine.
#2- To the program receiving this phone call, the thought So why dont you want your own applicant? could cross their mind. However, if the person who is calling on your behalf is able to communicate something convincing (your spouse has already matched at their program, your family is from there, etc), I think this issue would be avoided.
In summary, asking your program to call another program on your behalf has the potential to burn TWO bridges. An applicant is lucky to match into dermatology, no matter the program.
In my opinion, The IDEAL situation is to develop a strong relationship with a clinician-educator who is well connected with a reasonable number of programs yet loosely connected with your home program. Such a person has the goal of helping you to match into dermatology- no matter the program. I had the good fortune of having such a mentor. He would frequently check in throughout the application/interview process. On more than one occasion I informed him that a few programs that I was interested in (and had specific interest or a mild connection with) had sent out their first round of interviews but I had not yet received a rejection. In response to this information, he usually offered to contact such programs.
Other helpful information can be found here:
http://www.derminterest.org/phpbb3/viewtopic.php?f=8&t=178