Nonsense. The governor of Kentucky asked the legislature to call a convention to vote on secession, but they refused, and the subsequent election in June of 1861, Unionists won 9 out of 10 of Kentucky's congressional seats. They did ask to remain neutral, and the Union respected that until the south broke the truce by invading. After that, a group of pro-southern politicians gathered and announced that they were now the government of Kentucky, and they voted for secession. The confederacy did, in fact, admit them, but they were basically powerless and fled the state when the confederate invasion withdrew.
If they remained a part of the union why then did Grant occupy Paducah?
Again - this reinforces the point that Kentucky was not a union state at the start of the war.