Job related question:  Does this deserve to be hung up on?

I work for a very large medical company and we're on the phones all day long with patients and doctor's offices providing free medication to those who qualify for it.  We are bound by HIPPA regulations and are limited as to what we can say and to whom we can say it too.  I guess one of my biggest per peeves is someone calling me about a patient and they are on a speaker phone.  I don't know who's around them so when I give out patient info I would rather it be with the person I'm speaking with and they have the phone up to their ear.  I got a call this morning and a woman was calling about a patient and you could tell she was on a speaker phone.  Papers were rustling and her voice was trailing in and out like she was walking away from the phone then yelling back at it.  I politely asked if she was on a speakerphone and she said yes.  I then asked her if she didn't mind picking up the receiver because I wasn't comfortable giving out patient information on a speakerphone where someone else could possibly hear.  I didn't know if she was in an office with others listening or home in her bedroom with other family members close by.  Yes, she could have been alone but I wasn't willing to take that chance, again, HIPPA regulations.  When I asked her she then hung up the phone.  Was this really worth being hung up on?