Adobe Acrobat Reader is a pretty big install but after doing so I was able to see the PDF file - and its embedded video - just fine. There was a catch though; Acrobat is slower than Preview and now it was my default PDF viewer.
For the life of me I could not figure out how to make Preview my default viewer again. I right clicked on a PDF file and from the pop-up menu selected Open With - the sub menu that appeared allowed me to open it in Preview but not set that as the default.
At this point I did what I always do - Google up the problem and look for a solution. One of the first solutions I found was to use RCDefaultApp - a preferences pane add-in that allows you to see and set the default applications for file types, MIME types, etc. It worked great but I kept thinking that it was silly that I would need an add-on in order to do this. I am going to keep RCDefaultApp around though - it's pretty handy.
Finally, the way to do it in OS X
I finally managed to find it with a little more Google work. Right click on a file, select Get Info and, at the bottom of the Get Info window was an "Open With" area. From there I could see and set the default viewer and also click the Change All button to change it for everything.
Not long after I put this up Jerome put in a comment that you can hold down the Option key while right clicking and the menu selection changes to Always Open With - no need to even go into the Get Info window. Thanks Jerome!
Now I can see my PDFs quickly in the native Preview application and use Acrobat Reader when I need the extra features it affords.