It wasn't really lies, but a simple fact that BA call centre staff only have a certain amount of knowledge and training and the only real answer the agent could have given was "I don't know", especially for a more complex/rare situation such as yours.

But agents don't like to say "I don't know", and neither passengers nor their managers like to hear it, so they try to explain things to their best of their knowledge and end up getting themselves tied up in knots.