I don't know about your side of this scenario, but I work at a call center and we're told its illegal for us to give out any client information to anyone that calls, unless the caller can provide fairly strict verifications. At some point they even gave us the name of some fairly new legal act that made it illegal to do so, but I can't remember what it was(this was a few years ago).
Of course, that's from the business side, and just because we're told that doesn't mean its true..
So it may be illegal for Walgreens to be giving you this information, in which case Walgreens should be the concerned party- but I also don't see Walgreens making a big deal about it because they wouldn't want the publicity