Maybe US is more conversational when within its borders
Even if you go for the commonly abbreviated "The U.K " does the "the" suddenly not count? "The UK" also does not include Northern Ireland, which is part of Britain, which "The UK" is commonly an accepted type in for.
Can't agree on "US" being an acceptable answer. The country's name is "The United States of America" even if you're ignoring the "the" that STILL isn't two words.
You need to specify in the instructions that you are making an exception for these two. As someone else pointed out Sao Tome et principe is almost uniformly known as "Sao Tome" yet it isn't accepted.
It's a great idea for a quiz, but you have huge consistency issues.
I feel like with all the technicalities that gets confusing.