I have two applications on my Mac that will open DICOM files: OsiriX and Horos.
In response to a download and display request in Safari, I get the message shown in this screenshot:
The request is:
(XXXs for anonymization purposes)
It previously would simply download the data into Osirix and display them. Now, suddenly, I get the option to open the data with Horos only.
This doesn't happen with Chrome.
Update 12/22/16: It's happening with Chrome, too. Chrome opens the Horos app.
Second update: 12/22/16
Firefox Preferences still permits explicit specification of Applications. When I checked this, I got the following:
I changed this to "OsiriX" which has solved the issue for that browser. So, I've confirmed that "something" has set Horos.app as a Default. I just have to determine how to change that.