That's my point exactly. Turns times are not an indicator of success rate. I'm not saying faster turn times guarantees losses if you fail. I'm not trying to prove a negative here.
The factor isn't turn time, it's turn time AND raw infrastructure. Those two are always opposed due to opportunity cost. So, to the degree that your pursuit of turn time has hurt your infrastructure, your victory is less secure. But, to the degree that you've shaved off target turn time, you have those extra turns to produce. Security is lost at the point where production x turns needed to win for the faster turn time strategy is lower than that of the slower turn strategy. This happens more often than you think, not just on the extremes. It's with every decision you make in the game. This consideration only disappears when you are at 0% or 100% victory, at which point like I said before, turn times, like anything else in this game, becomes just style points.
Agree. This is especially true for deity CV (when to build the music guild for example?); surety/certainty of victory depends on your maximum tourism once all modifiers are in place, as well as partially on speed, but that shouldn't be a factor unless your tech is exceptionally slow.
On the other hand turn time/speed depends on the rate of your tech/SP and random factors such as what AIs do to each other.
A rough example:
You can win pre t200 with 250-300 tpt with +10 faith output by GS rush and then GM rush; you went for a full-blown science game ignoring religion and most wonders (however, miss it by a hair, and your last civ enters a golden age where your influence is no longer rising... you are screwed)
Or you can win at t250 with 500 tpt and +40 fpt (your tech was delayed because you did not ignore religion/religious wonders for example) but even if something unimaginable happens (your last civ gets embargoed, they DoW you, etc.) you still could buy one more GM with faith just in time to win.
Or you can win at t280 with 700 tpt and +100 fpt (no matter what the other civ does, unless they wipe you out/launch their ship) victory is almost 100% certain. You were slower because you spent your energy and hammers wonderwhoring and delayed universities for workshops etc.
Of course you have to know when you've crossed the line; if it takes you 320 turns to get everything in order (internet NVC airports all SP) before you stream your GM, then victory is no longer certain. Speed is certainty to an extent.