If Kirabati changed its times, part of the country would have been GMT-12 and the remainder GMT +12, which, though I like the theory, does not fit the question.
The celcius/fahrenheit suggestion is inspired - well done! Unfortunately history suggests that countries tend to go from Fahrenheit to Celcius, not the other way around. I will persue this line of though however and report back!
prior to 1/1/95 parts of Kiribati were one side of the International Dateline - parts of it were the other side. The local powers that be decided to shift the dateline to allow all of the islands to be in the same time zone. As there is no international law to force any country to accept 'international' definitions of time, then parts of Kiribati went from 10 hours behind GMT to 14 hours ahead (and, yes, it does not conform to the 'standard')