The headline is not a hundred percent correct. Only avoid flight connections in the US if you are inbound on an international flight from outside the USA. This is because if you connect in the US, you have to pick up all your checked bags, go through security and check your bags again. It doesn’t matter if you are just in transit in the US, for example you are flying from the UK to Brazil and have to change plane in the USA, or you travel to a city in the US but have to connect to another flight somewhere in the US before. Example: You are flying in from Europe and want to go to San Francisco but have to change plane maybe in Washington D.C.
There is only one exception so far and that is the Atlanta Airport (ATL). On my travels from Germany to Panama and back I didn’t have to recheck my bags. You will get some additional purple tags on your checked bags at your origin airport and the agent will also tell you about this. Other than that I try to connect outside of the US and from there fly to my final destination. This also only works if you are going to a major city like New York, San Francisco, Seattle, Los Angeles and so on.
If you are going to a small town with no international terminal you won’t have any other chance as connecting in the United States.
If anybody has experience with other airports, which will transfer your bags to your final destination, let me know in the comments.