That's the stiffness of the material, but what matters in a frame is the stiffness in bending, and the deflection of a tube varies with the cube of the length IIRC.
The key words are deflection over length, as you point out. But I'm really onto the point about frame stiffness and the nonsense spoken about it. First of all stiffness is moot at the levels we're talking about but I want to see someone say that a frame made for 23mm tyres is stiffer than a frame made for 28mm tyres. We're talking about 1.5mm difference in each of the three dimensions at the points where the tyre could touch the frame. Even if you cube that, you still get....zero-ish.
The real reason in the days of steel was that extra clearance required a dimple in each of the two chainstays and possible in each of the two fork blades. Framebuilders preferred to use straight tubes and save some labour.
Today's mould-formed composite frames? I can't think of a rational reason why they would restrict tyre width that much. I've seen arguments of improved airflow, stiffness (obviously, stiffness is the holy grail of explaining everything) and restrictions for brake caliper opening. None of these make sense. There's even a trend to slam the back wheel right up to the seat tube (and into a niche carved into it) so close that grit scrapes the frame. This I've seen justified as a measure to "improve climbing", I kid you not.
We shouldn't eat the rubbish the industry feeds us. However, once the industry has the upper hand and you have no choice anymore, you will be force fed.