Oh no it doesn't.
I guess you are sort of correct. I over simplified. In HD video, we use REC709 space. It has virtually the same white point and gamma as sRGB. Black and white levels can be different, but one can deliver in "REC709-full range".
And yes, the truth is, that there is no standard gamma in REC709 video either...it's up to the user to set to match their viewing conditions. Usually 2.2 to 2.4) My newish HD tv at home came preset to gamma 2.4. (but I must add that it looks rather closer to 2.2, when set at 2.4!)
And while I'm on the subject,
, I sometimes color correct feature films (usually one's I've photographed) and we work in, gulp, REC709. But release in PCI-d3 space (which is a little bit bigger)
Why? I've got 3 deliverables: Digital movie theaters, film prints for the few theaters that still show them, and HDtv. My sRGB/REC709 calibrated display shows a gamut that fits entirely into P3 space for digital theater. My work will be viewed identically at the theater after a proper color space transform.
The film print is a different animal entirely. The color space of a film print is quite bigger at certain saturated colors. But the space is quite smaller in many dark colors, especially flesh tones. My film print, after our best effort at color space transform, will be limited by the INTERSECTIONS of the REC709/sRGB and film print color spaces. But, you know what? It looks pretty darn good when done well. Nobody complained when they saw Titanic, and every digital effect shot (the majority of the film) was done just this way
.
In the end, when I work in REC709/sRGB, I don't need to do a trim pass of the whole movie to shoe horn it back into REC709. (we have LUT's for the conversion, but sometimes when there is a lot of out of gamut color, you need to adjust the look). And, the film print is what it is. We assume it's shown in an old theater, with a dim lamp, and cheap tickets...