Stiff but flexible

Maybe it means that the bars cannot extend, but can bend?

No, 'stiff' definitely doesn't mean 'inextensible'. I think the writer was trying to say 'flexible, but not too flexible'. Perhaps so that people wouldn't worry?

Well, if you're talking about a spring, "stiff" definitely does mean "of limited extensibility". (Actually "limited" is not a good word. A stiff spring can in theory be extended indefinitely, but it requires a large force to do so.)

As an editor, I would have recommended something like "strong but flexible" or "firm but flexible."

Now that I have had a minute to think about it, though, I wonder how one would describe rebar, the metal rods used to reinforce concrete. "Stiff but flexible" sounds like an accurate term for them.

'Stiff but flexible' may be evocative (as only an oxymoron can be), but how can it be accurate if the two terms have exactly the opposite meaning?

shilgia #3, you are right about stiff springs. But their inextensibility is a consequence of their stiffness, because they are helical. I don't think the Statue of Liberty is supported by springs.

Sorry, I can't back down, especially now that I have looked up the meaning of "stiff."

My dictionary gives "difficult to bend or stretch" as the first definition, "rigid" as the second.

No, but it may be supported by something akin to springs: a material that is hard (but not impossible) to compress or extend, but that may be able to bend a bit to keep the statue intact under small temperature differences, vibrations, and such.

Alternatively, they could be using "flexible" as an antonym to rigid, not stiff. Rigid and stiff are sort of the same thing, but something that is rigid cannot change shape at all, while something that is stiff can only do so with great difficulty. So something that is "rigid but flexible" may not exist, while something that is "stiff but flexible" is something that can bend, but only a little bit.