I have the exact same issue. I have an updated ADR, TrueView, and an expired trial of Autocad 2013 installed.
I was able to open DWGs by right clicking on them and choosing Open With>TrueView.
With Design Review AND TrueView installed (and possibly working together), can I open DWG files and "red line" them? If so, does it convert the DWG file into DWF before I can "red line" them?
Background: Even though I know AutoCAD very well (I teach night classes) they won't let me have AutoCAD here at the construction site of my day job, for some reason. I've been using TrueView to examine contractor dwg files. I need to upgrade TrueView to see new R2013 DWG files, and I figure I might as well get Design Review so I can mark up drawings (assuming I can) , not just alter layers and save as .pdf.
ADR only works on DWF files: if you want to 'redline' DWG files you must use a program that reads and writes DWG (aka AutoCAD or others). Trueview is a viewer with printing and conversion abilities only.
Autodesk does not offer any free backdoor way to edit and markup DWG files directly unless you all want to explore using www.autocadws.com online (a great tool IMHO that is still free) or through collaboration in Autodesk 360's cloud if you all are on current AutoCAD versions.