PDF opened outside of application when earlier versions of Adobe Reader used

I have this strange issue where when I use an early enough version of Adobe Reader, PDF's that are embedded in an iframe in my web application end up being downloaded in Adobe Reader instead. The web application supports IE only (I know, bad, but I did not design it originally). So I don't know if it happens in other browsers or not. Later versions of Adobe Reader do not have this problem (11.0.7+ in particular). In my C# web application, I have a simple WebBrowser control that displays a web page which contains the iframe.

I have researched everywhere online about this. I noticed that the WebBrowser control is rendering the web pages using the IE7 rendering engine. So I figured out how to force it to render in IE11. That didn't fix the problem. I'm wondering if there is some other IE related thing like this that might be causing this problem with earlier versions of Adobe Reader? Is it something security/permissions related that is causing the PDF to be downloaded instead of embedded? What else could it be?