I have set captions on and I have set captions off on both Hulu and Showtimeanytime. No matter what setting I use, the captions do not display. The movie does record. When I use a plain browser to access the same movie on Hulu or the same movie on Showtimeanytime, setting the captions to "on" works and I see them. Somehow, your DVR is blocking open captions.
It is not possible to DVR capture subtitles unless they are part of the video and not a web page artefact.