Yes, but the code has to understand and model the input into a program representation: the AST. That's the essence of the "parse, don't validate" paradigm. Instead of looking at each piece of a blob of data in isolation to determine if it's a valid value, turn the input into a type-rich representation in the problem domain.
In the case of the FPRSA-R system in question, it does none of that. It's simply a gateway to translate data in format A to data in format B, like an ETL system. It's not looking at the input as a flight plan with waypoints, segments and routes.
Why the programmers chose to do the equivalent of bluescreening on one failed input, I can't say. As others have pointed out, the situation it gave up on isn't so rare: 1 in 15 million will happen. Of course switching to an identical backup system is a bad choice, too. In safety-critical work, there needs to be a different backup, much like the Backup Flight System in the space shuttle or the Abort Guidance System on the Apollo Lunar Module: a completely different set of avionics, programmed independently.
THAT SAID isolation of the decoding code and data structures, having a way back to either checkpoint/restore or wipe out bad state (or, proving the absence of side effects, as SPARK dataflow contracts allow, for example) is better design, I wish would be taught more often. I really dislike how often exception propagation is taught without showing the handling of side effects...
I feel the lack of investment in destroying the parsing- (and validation-) related classes of bugs is the worst oversight in the history of computing. We have the tools to build crash-proof parsers (spark, Frama-C, and custom model checked code generators such as recordflux) that - not being perfect in any way - if they had a tiny bit of the effort the security industry put in mending all the 'Postel's law' junk out there, we'd be working on other stuff.
I built, with an intern, an in-house bit-precise code generator for deserializers that can be proved absent of runtime errors, and am moving to semantics checks ('field X and field Y can only present together', or 'field Y must be greater or equal to the previous time field Y was present'). It's not that hard, compared to many other proof and safety/security endeavours.