When I read this, I was reminded of instances where I have heard something different from what was actually said.
Did they lie? Did I misunderstand? Did they forget what they said? I don't know. I just know that it wasn't clear to me.
Can you give more details? This questions begs for specifics. Otherwise, I just refer to my experiences, which are probably nothing like yours.
When dealing with very defensive people who routinely also lie in order to hide their defensiveness, I realise that some become very practised at speaking in riddles, deflecting questions and dodging issues.
They will say anything that comes into their head to put off being direct or straightforward. Unless they have a perfect recall, they can get found out, but it requires almost forensic logging of what they previously said, because they can sound so convincing.
Someone I know is so skilled at dodging and hedging that she has become a virtuoso at doing this. She can completely contradict what she said the day before and then make you feel that you misheard the first time, or that you didn't take in what she said. In fact you did listen first time, but she's convinced you that it's you that has the problem.
I got taken in for a long while, until I started really concentrating on everything she said, then began to confront her about these deceptions. Once she was rumbled, she attempted to change the subject or went silent, desperately scrabbling around for a new angle. Bingo! Her new angle was to project back on me my exact criticism of her. I said she was controlling, and now apparently I am controlling. I said she was spiteful, but now I am apparently spiteful.
In the field of defensiveness and resultant deception, some people have spent a lifetime improving those deception skills. They are very hard to deal with.