Held into what?
I have been inside several computer CRT monitors and they all bolt the CRT's band into the bezel. The bezel is then connected to the base where the stand is attached. You clearly can't support the tube from the bottom, you have to support it from the front.
On older TV sets I have seen (1940s), there is frequently a support around the gun area. I have never seen anything like that in a 1970s or later display.
To the OP, the antireflective coating is what generally picks up scratches. In some cases the glass may be scratched, but remember that it's barium-lead doped glass and is hard and dense. Either way, there is nothing you can do to remove the scratches. Don't under any circumstances try to polish the glass, it will absolutely ruin it. Get used to the scratches and you'll find they are not very visible after all.