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And still this question is raised.

No, moly is not more rigid than mild steel. The elasticity of all steel alloys is almost identical (Young's modulus: 30 × 10^6 psi).

"I have always heard that moly is twice as light, and twice as strong."
No, moly is not lighter than mild steel, the weight difference is only 1-2% depending on the exact alloy. The reason it's lighter is smaller wall thickness - that's it.
No, moly is not twice as strong, it's about 30% stronger (not stiffer), and that's if properly welded and heat-treated. If the wall thickness is reduced to save weight the strenghs are about equal. You can have more strength with the same weight, the same strength with less weight, or some intermediate.

Re: "they don't want them trying to weld chrome moly with a OX Acetelene torch"
Guess how Reynolds 531 chrome-moly chassis (including Formula 1 back in the day) are built for road racing? That's right - gas brazed with a torch. Read Carroll Smith.

"both these mild steel cages deflected WAY too much for safety"
That's not what did it.

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And why do you say its not stiffer, it takes a significantly
greater force to bend it on a bender over the
mild steel?

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From your first picture it is a prime example of improper installation.The piller bar is layed back way too far and is attached at the side of the halow bar.It should be attached at the underside of the halow to give any support.Many times an installer will try and follow the windshield and body contours which make the angles less effective for support.NASCAR uses MS cages for impact absorption(give)CM is lighter and harder and has little impact absorption quality.CM is more prone to break rather than bend.And because of it's hardness it will fatigue from twisting and loading in time.This is why prostock,top fuel and other classes constantly update their chassis.If you have ever seen a CM Chassis wrecked you will commonly see tubing breaking not at the welds but in the tube body.And also a good oxy/ecty welder can weld CM just as good as a good tig welder.A furthur note,with all the approved and new welding techniques CM can be mig welded to perfection,NHRA just doesn't allow it.They fear that that fitment would be compromised buy the ease of application of mig welding,where as you can't very well hide gaps with the tig process.Structural design, effectivness,fitment,weld and application are all important part of how you choose material and build a cage or chassis.

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BG and polyspheric
Great job in properly explaining the "CM/MS Myth's"

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You brought up DOM tubing, problem is, 90% of people who use MS don't use DOM, they use cheap, welded seam MS. A well built DOM cage is as strong as anything else and DOM costs nearly the same as Moly. I personally used DOM on all my MS cages, but when I got to the point that I no longer MIG welded any cage, regardless of material, it made no sense to not use Moly. Makes the car lighter and worth more for resale. I don't care what the cert is, a Moly car will always bring more. I would not put MS in a new car period, but that's just me.

Monte

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The cost of DOM(drawn on a mandral)MS to Aircraft quality CM is 1&1/2 times cheaper,we buy direct.Rolled and seamed MS is the cheapest tubing available.There are many different quality specs for either,varying the cost.We use DOM-MS and AC-CM for our custom chassis and cage work.We don't push our customer either way,we educate them on the pros and cons for their particular application and cost budget.We let them decide.Our 68 Cuda dbl rail/strut chassis car and our 65 Dodge a-arm car are both MS.We have 5 cars in the shop for up-grades,of the 5 three are MS and 2 are CM.4 of them are certified to 7.50.Go figure?