You're assuming that he's alluding to the fifth amendment, the Miranda warning is just a notification of it
Exactly. Each country phrases its notification of rights of the accused differently. For example, the police caution in Great Britain begins "You do not have to say anything." Use of a particular country's wording alludes to the statutory and case law regarding the rights of the accused in that country. For example, the police caution used in England and Wales since 1994 includes "it may harm your defence if you do not mention when questioned something which you later rely on in court", a concept of guilt by omission that doesn't apply in the States. This difference was a plot point in an episode of the first season of Life on Mars, if the trope page about the British caution is to be believed.