I think that's going a little too far. If you can construct a "rigid beam" five feet long, I see no way that relativity countermands a "rigid beam" 25 million miles long. It's just that "rigid" doesn't mean what grandparent thinks it means -- info still travels through the beam via pressure waves.
The pressure waves are ultimately manifestations of the exclusion principle, expressed through forces that are constrained to travel at or below c.
So yes, relativity dictates that you can't create a rigid beam 25 molecules long, much less 25 million miles long. There can be no such thing as a perfectly rigid beam of any length.
Exactly, you can only construct beams at any scale that seem rigid at some scale. A 2 foot long piece of re-bar looks pretty rigid, until you look closer.