farci,
The harsh reality is that documentation is and shall remain the passenger's problem. It would also require substantial amounts of new business-logic to be implemented on their customer-facing systems. Plus you would be faced with a situation where those passengers with a few missing brain cells would assume that because the airline says its OK, you'll have no problems ....
The fact is that documentation is a battle you can't win either way and you're at the mercy of the system at all times.
At one end there are cases like yours where documents are obviously invalid. Something that you'll have to take on the chin, lesson learnt the hard way.
At the other end, you have cases like a colleague of mine who travelled to Israel, she checked expiry validity requirements, found her passport didn't meet them, went through the process of getting a new passport, entry into Israel was not a problem, but on departure from Israel, pre-screening took issue with her fancy new passport and subjected her to the whole nine-yards (questioning, bag search etc). She is of a pristinely clean background, the only flag the Israelis went by was her brand new passport that was renewed only a few weeks before her departure to Israel.
And then there are the whole variety of scenarios in-between.
So, as I said... you can't win, all you can do is check compliance with documentation requirements, resolve issues and then hope for the best !