Most people do use a PVR or some capture card but as a rule of thumb if something is built into a TV or device and does not explicitly state you can capture input (mainly for things like older/DV video cameras) you probably can not. Your best bet in that situation is to pull it apart and hope it is just a couple of standard devices glued together and then attached with a common protocol* (in your case HDMI or some high level component) you can intercept instead.
It would certainly not be the first time a common protocol has been used internally for something (maybe with a custom connector)- the original xbox controller was USB, the 360 hard drive (laptop sata), the 360 DVD drive (also sata), most older hifi stacks and car CD players (plain "phono" grade audio), wii controller extensions (basic tweak on I2C) and so on but for this sort of thing I would not count on it (HDMI or perhaps more appropriately HDCP have had devices that allow trivial workarounds/intercepts but far more are done properly).