It seems that, for photo, it's better to shoot high ISO in camera. That's what a Google search tells me anyway.

But I'm having trouble finding answers about video. Is it better to raise ISO at time of shooting, or boost in post, or do you get the same results either way?

You should not underexpose your video image. If it's the difference between raising the ISO, or underexposing your video, raise the ISO.

My understanding was it matters how close to correct your exposure is. For instance, slightly dim is fine, but at some point on the curve, the value of low-noise iso is gone because of how dark the image.

Boosting video levels means using electronic gain. Gain amplifies both the desired image and the sensor noise. High ISO settings in the camera add gain and are equivalent to using the boost switch on a traditional video camera. If you boost levels in post production then you amplify the desired image, sensor noise and artifacts from the video compression system. In general, using high ISO/video gain in the camera before compression yields better results. Remember that using gain can lead to clipping in brighter parts of the image so make sure you consider the balance between overall higher brightness and highlight reproduction.