It's seriously difficult to understand the mindset of the organization and how they came into this. Did they even bother hiring a competent cryptographer when designing their product ? Were they duped by someone they hired and led to design a insecure product ? Or is encrypting an RFID communication a difficult and non-trivial task with no known vetted solution ?
I don't think that the problem is difficult in some fundamental way (the problem of verifying a remote host with asymmetric crypto has been reasonably well explored with SSL/TLS, and an access control system has the advantage of being able to trust only a CA it controls, and the advantage that you need to get physical access to an RFID reader pad to attempt attacks); but there are significant practical challenges.
RFID chips are pretty power constrained, since they only get whatever energy they can scavenge from the reader's RF output; and customers want them to be cheap. The industry also has fairly long product lifecycles (since, once you've put in a zillion card readers and integrated it with all your other building security stuff you don't want to rip it out and upgrade in 2 years).
It isn't so much a 'there is no known cryptographic solution to this problem' issue as a 'Why yes, we still have major customers using the 'security' provided by the lousy proprietary cryptosystem that our engineers were able to cram into a cheap, power-constrained, chip using the fab processes available in the mid to late 90s, and we really don't want to fix that' issue.