Plus: was the letter only sent to or was it sent to everyone who was doing the quiz? If everyone has been snapped at, this is reflecting more on the boss than on the team, who is clearly losing his/her grip on things. If you have been singled out, you need to take this up with your boss, HR and your union rep.
Depending on the type of organisation you are in, it might be worth contacting whoever sends out the newsletter and innocently describing the trouble it has landed you in. Ask them to please make it very clear that it is not to be engaged with during work time. This might then lead to a word being had with your boss, especially if the newsletter is seen as an important arm of 'corporate mesaage'.
Also, how are your break times arranged? Do you move away from your workstation every couple of hours or is it usual to take your breaks at your desk? If the latter, how did your boss know you were not on your break when doing the quiz? Another matter to discuss with HR.
At the end of the day it is up to the firm to enforce good management practice and if they don't, or if they actually think this is good practice, then there is not a lot you can do.