As a radar controller in Canada, if I issue a clearance or instruction and your read back is not correct and I don't catch it or correct it then the blame for the error is on me. It is the controller's responsibility to catch and correct read back errors. If an incident subsequently occurs then an investigation will be carried out. If it turns out that you (the pilot) did what you read back, even if that differs from what I said to you, then you are not blamed for the incident. If you do something different from what YOU read back, then you are blamed.
That said, even though you aren't at fault it's just another "hole in the cheese" if you don't question things when they seem wrong. You've already indicated that you do this already so it's not due to laziness or nervousness on your part, you just happened to be very busy at the time and that's understandable. Legally speaking the error in this case is on the controller (more specifically, the instructor and not the trainee).
Of course, maybe the rules are different in America, I don't know for sure. Anyway, keep up the good work with your videos - even though my airspace starts in the flight levels they provide some interesting insight into the life of a pilot.