There are, as always with articles (and proper nouns), idiosyncrasies.
Entities which are not usually known by their abbreviations tend to keep or omit the articles in parallel with the long forms:
The National Symphony Orchestra is conducted by Christoph Eschenbach.
The NSO is conducted by Christoph Eschenbach.
Doctors Without Borders is based in New York City.
DWB is based in New York City.
But where an abbreviation is widely known, it is like an alternative name— and thus, whether or not the abbreviation takes an article is unrelated to whether it does so when spelled out, and is largely a matter of convention:
The BBC was chartered in 1927.
The British Broadcasting Corporation was chartered in 1927.
NBC introduced its trademark chimes in 1931.
The National Broadcasting Corporation introduced its trademark chimes in 1931.
We generally say the United Kingdom and the United States, the U.K. and the U.S. / the U.S.A., and I think native English speakers from an early age learn to silently read the United Kingdom and the United States whenever they see UK and US. Not to do so sounds unnatural, since this is the convention.
Others, however, may tend to read UK as an alternative name instead of instinctively reading it out, in which case the UK could indeed sound strange, like saying the CBS or the UNICEF.