*You* are correct.
Capital can be a noun or an adjective. Capital can refer to uppercase letters, accumulated wealth, *or the city that serves as the seat of a country’s or state’s government.*
A capitol is a building in which the legislative body of government meets.
In the United States, the Capitol is a building in Washington in which the US Congress meets.
https://www.grammarly.com/blog/capital-vs-capitol/
And the ESL students at the Consortium CONTINUE to try to explain English to me...