While the question is about exaggerating a response, the examples given seem to be more about active deception (particularly in the police officer example). A few words could help explain:
verb (used with object)
1.to represent fictitiously; put on an appearance of:
to feign sickness.
2.to invent fictitiously or deceptively, as a story or an excuse.
The soccer player was feigning his injuries.
verb (used without object), dis·sim·u·lat·ed, dis·sim·u·lat·ing.
2.to conceal one's true motives, thoughts, etc., by some pretense; speak or act hypocritically.
"Woah woah woah, calm down", the police officer responded, dissimulating.
See also dissemble.
Additionally, a charade, can often involve using exaggerated actions or appearances for the purpose of deception.
- a blatant pretense or deception, especially something so full of pretense as to be a travesty.