Upvote:8
The comments all assume that the legal obligations between the airline and the ticket agent are the same in Uzbekistan as in the US or Europe. In the US and Europe, the passenger bears responsibility for the correctness and completeness of travel documents.
That the travel agent was fined, however, suggests that in Uzbekistan the obligations between the parties are different. Perhaps the ticket agent really is liable for the error; perhaps the airline is just charging the ticket agent because it (the airline) is more powerful than the agent. Perhaps the "fine" was imposed by the government, not the airline, for a violation of Uzbekistan law. We don't know.
I agree with the comment of @Arthur'sPass: you should consult someone familiar with Uzbekistan law and practice, likely an attorney or solicitor in Uzbekistan.
EDIT Dec 6, 2019:
The answer to OP's dilemma will be found in some combination of: a) Uzbekistan Airlines' Terms of Carriage; b) the contractual relationship between Uzbekistan Airlines and the OP, or any Uzbek law or administrative regulation which affects that relationship; c) the contractual relationship between the traveler and the OP, or any Uzbek law or administrative regulation which affects that relationship; and/or d) how things are actually or usually done in Uzbekistan.
I don't know about any of these matters. The OP needs to talk to someone who does.