I've had cross-talk happen while on a cellphone. It cut over to another voice saying "... three months!..."- it sounded like an ad. But it wasn't audible on the other end and the conversation wasn't interrupted.
The question you should be asking is: What are the odds that some random vocal sound might be interpreted as "liberty" by a human brain that is primed by talking about that subject?
Never did work out what happened there.