Everytime this is posted I feel the need to mention to Brits specifically: this does not apply.
"It may harm your defence if when questioned you fail to mention something you will later rely on in court".
Failure to answer can seriously harm your defence and I've heard of people I personally know (though I wasn't in the courtroom) where the prosecution hammered the point that they "came up with a plausible sounding story" after the arrest.
Obviously Border Patrol is not the same as being arrested; but this is an important caveat for the video posted.
Talk to british police. If you feel like lying, keep your story straight or give basic facts.