I've seen a 5/8" bar dig a groove in the concrete at about 3500 RPM because it was long enough to reach the floor. The operator steadied it with his hand and was satisfied that it was straight enough to run balanced......WRONG. It bent as soon as he started his cut.
I've also seen a rotor from a 2 7/8" mud motor disappear from view about the time the operator was bringing the tool up to touch off for facing. These rotors are about 9 feet long. Bent it up pretty good and beat the control cabinet for the M-5 which was positioned just to the left of operators position. I would blame the lack of support in the spindle and/or low chuck pressure on it.
In both cases, a headstock spider was not in use. Personally, I don't think it would have made any difference. I have run small diameter stock, which of course normally likes high RPM, sticking out of the back of the chuck but not the spindle, fast enough to flex over and stay in contact with the spindle bore. Vibration was noticeable, but the lathe heavy enough to handle it. I didn't like it though, so stuffed some shop towels around it just enough to keep it roughly centered.
The 3:1 "rule" is more for control of pushoff and chatter, IMO. If you are just center drilling, you can get away with much more if you are careful. Just no high speeds. Turning or boring, etc, the less the better is all I'll say. As far as the back of the chuck, you have more leeway, and the concern there is likely more about control of concentricity along the axis of the part/material. Mostly a judgement call, other than case similar to what I mentioned above.