Apologies for trying to offer an answer to a nearly three year old question, but I'm unable to resist this one.
The truth is that all spacecraft that operate (however briefly) in our atmosphere do need to be concerned with aeroelasticity. It is only through careful design, analysis, and testing that a vehicle will be free from catastrophic aeroelastic effects -- it certainly doesn't happen by accident.
As you noted in your link (NASA TM X-2570), there was an entire session devoted to aeroelastic effects on the space shuttle at a single joint NASA/AIAA conference in 1972. Slide 28 of the PDF is particularly interesting because it clearly shows that the biggest challenges for shuttle flutter analyses were in the transonic regime, not necessarily the hypersonic regime. This is largely true today and the explanation is probably telling. In exterior hypersonic flow, the forces are generally fairly steady and (on surfaces facing the freestream) typically very readily obtained (e.g., using Newtonian aerodynamics -- see NASA TM X-53391). Transonic aerodynamics, however, are highly nonlinear and required modest computing power to evaluate that didn't really become available until the late 1980s (e.g., Silva and Bennett, "Using Transonic Small Disturbance Theory for Predicting the Aeroelastic Stability of a Flexible Wind Tunnel Model", 1990).
If the question is really "why don't we see aeroelastic failures of space planes?", the answer comes back to all that careful analysis, design, and test. Space programs in particular are extremely thorough about working through every possible issue before flight. I've heard this derisively called "analysis-paralysis" and some of the criticism leveled at the time and budget required for space vehicles may indeed be fair. However, unlike their air-vehicle counterparts, which have the ability to slowly expand a flight envelope guided by analysis during flight testing, space vehicles are usually an all-or-nothing. Thus, there is a ton of time, man-hours, and money that go into ensuring that these vehicles are flutter-free.
Having said all that, it's not that space vehicles are actually so well understood that they never suffer from unexpected aeroelastic problems. Indeed, it's not uncommon that they do encounter these types of issues as they transition from static, to low-speed, compressible, transonic, supersonic, and finally hypersonic flight regimes (or vice-versa on entry). Thankfully though, the issues encountered have historically not been catastrophic (did I mention the enormous amount of effort that went into design, analysis, and test?). However, when these issues do crop up, they are assiduously examined post-flight and the vehicle typically will not fly again until the issue is expected to be resolved.