A US bank says it can't send an international wire transfer even though it goes through a US correspondent bank with a US swift code

Question

I am trying to have money wired from a small bank in the USA. I was told they couldn't send money out of the country but as the money has to go through a correspondent bank in the US with an American swift code, I can't see what the problem is. They are not sending money outside the country but simply out of state.

Not sure how to proceed.