Any truth to these two stories during Apollo development?

[Everett]

One thing about the possibility of a 4 SIC retro/one retro failure to fire recontact possibility - what's are they referring to when they talk about the "3 G case?"

About saving weight on the booster - this could be referring to when they went from the Saturn C4B (4 F1's) to the C5 (5x F1), or when they took that and improved it into the final Saturn V by increasing the second stage propellant load and increasing the diameter of the SIVb. (Possible because that hasn't gotten to the metal cutting stage yet.) Also, for building the ISS, they improved the shuttle payload by lightening the external tank by 3500 kg simply by changing to a different alloy. On a booster the size of the Saturn V, I'd imagine a similar alloy change could easily increase payload by a similar amount. (especially on the SIVb) Or by simply decreasing the thickness of a structural member by a tiny fraction of an inch, multiplied by a lot of said structural member, with the resulting decrease in strength being acceptable due to the booster already having a greater structural margin of safety than required.

[ka9q]

I guess when you're dealing with millions of pounds of vehicle going at thousands of miles an hour with three people on it

Actually, the problem is that it's not millions of pounds of vehicle. Or at least not nearly as many millions of pounds as at liftoff. Nearly all your propellant is gone so you're much lighter, so for a constant engine thrust they're producing much more acceleration (F=ma -> a = F/m). Any vibration or unbalanced thrust will have that much more effect on you than when you left the pad.

Remember the Saturn V shut down its inboard F-1 engine early, despite the decrease in performance from the resulting increase in gravity loss, to keep acceleration from exceeding 4 g and overstressing the vehicle. It was only about 1.1 g at liftoff...