I'm not sure where you heard that the strength only comes from the geometry of the tubing and not from the inherent strength of the material. Were this true then would could all be riding plastic framed bikes!
Let's discuss "strength". With bike frames, there's several important considerations. These are:
1. The tensile strength of the tubing, i.e. at what point it deforms or breaks
2. It's resistance to corrosion, i.e. does it oxidise or rust
3. Elastic modulus, i.e. the stiffness of the frame
4. Fatigue limit, i.e. the cyclical stress from pedaling or bumps
These are all inherent material characteristics, and are not related to the geometry.
Now let's look at the materials commonly used in bike frame manufacture.
Steel frames (i.e. Reynolds, True Temper, Columbus, Tange) have the highest density, and the highest tensile strength. It also has a high fatigue limit. This makes them (in general) the heaviest of the frame materials, but the strongest. This still has nothing to do with geometry. However, steel rusts like a 1980s Ford Fiesta at the seaside if not looked after.
Aluminum frames (typically 6061 or 7005 alloys) have a lower density to steel, and a lower tensile strength, but a higher strength to weight ratio. This means that an aluminum frame will usually weigh less and still be reasonably strong, but not as strong as a steel frame. The other advantage to an aluminum frame is it's optimal wall thickness, which allows aluminum frames to be oversized with thin walls, creating a frame that is very stiff. Aluminum doesn't rust. Traditionally, aluminum has a lower fatigue limit than both steel and aluminum, but this isn't always the case these days.
Titanium frames have are the best compromise of tensile strength, density and strength to weight ratio, but usually phenomenally expensive. The metal itself isn't particularly expensive, but machining it and working with it is. Titanium has half the density of steel, but has a much closer tensile strength, making it an ideal lightweight bike tubing, and is still seen by most as the ultimate material. Titanium doesn't rust and doesn't need to be painted.
Carbon fibre has an extremely low density, but can be formed and shaped and reinforced with extra layers in areas where stress is applied (i.e. the bottom bracket area). Under normal cycling circumstances, the tensile strength of a carbon frame is very good, as the frame has been designed to withstand stress of cycling by the way the carbon has been laid up. However, it's impact resistance is poor, as a crash can crack or even snap a carbon frame.
Now let's discuss geometry. The geometry of a frame determines a rider's position on the bike and the intended usage. Hence a road bike geometry makes for a more low profile position, whereas a mountain bike makes for a more upright position and compensates for the travel length of suspension forks. The geometry of the frame is not the deciding factor in the strength of a frame as most frames have the same double triangle design anyway.
I'm assuming you live in the US or Canada, because I can't find either of the bikes you mention, so I don't know if they are road or mountain bikes. Either way, bike frames these days are designed to stand up to abuse. We live in an extremely litigious society, and if bike frames were failing left right and centre then the manufacturers would go bust because they'd be sued all the time. However, let's be sensible. If you weighed 400lbs it would be a bad idea to buy a carbon fibre race frame.
My daily road bike frame is a Burls titanium frame, which ways about 2.5lbs. This makes it lighter than all but the most exotic steel frame, most aluminum frames and some carbon frames, but it is extremely strong and reasonably stiff. I wouldn't swap it for even the best steel or aluminum frame, and I trust it to haul my 252lb body over some of the worst roads in Europe, so I would say your lack of trust of lightweight frames is misplaced. A well designed, well made lightweight frame is as good if not better than a heavier steel frame.
I hope this helps!