Not true, really.
The States that seceded from the Union already held the view that they themselves were already sovereign States who had freely chosen to be a part of the Union with the other States. When they decided to no longer wished to be a part of this Union, they left it, as a sovereign State would have the right to do. Then, they freely formed the Confederacy with other sovereign States. States that left the Union after the Confederacy was formed did so under the pretext that they were sovereign nations, and then they joined the C.S.A.
However, to "change allegiance" you not first secede. A knight certainly does not secede from the realm when he changes his allegiance to another Lord, nor does a Lord secede from the realm before he changes his allegiance to another Duke. Similarly, a Duke need not secede from the realm before he changes his allegiance to another Crown.
The Founding Fathers actually
did word it so that the States were sovereign, united a federation with each other in a republic known as the United States of America. The old Articles of Confederation present this mindset most clearly. The centeralized government of the federal system was strengthened when the Constitution was drafted, but many States, especially in the South, believed in States' Rights. Even in the Civil War, most units were not under the mindset that they were American soldiers (on either side). They were, rather, Georgian soldiers, New Yorker soldiers, Pennsylvanian soliders, Texan soliders. We were, prior to the end of the Civil War, truly the united States of America.
I am digressing some, however.
Even if the States did view themselves as sovereign (which they typically did, even in the North), the Union was just that: A union of the States. A federation. As they were leaving the Union, they were seceding from it, no matter to be sovereign or join another polity.
And a secession is:
The action of withdrawing formally from membership of a federation or body, esp. a political state
With how the feudal hierarchy works, even the most strict monarchy is a federation of nobles. In history, the old Holy Roman Empire is a stellar example of that, being more of a confederation than a purely whole entity.
Within a polity, such as one of Battlemaster's realms, it is not secession. If a knight joined another region within the Kingdom by swearing fidelity to a different Lord, at worst it would be oathbreaking . At its best, the previous Lord would have consented to absolve the knight of his oath and it would be business as usual. Either way, it's not secession as lands aren't changing hands, only a single Knight/person. That'd be like me moving to Canada and getting made a citizen there. I'm not seceding as I'm not bringing any property with me. Not that I wouldn't be laughed at if I tried... Now, if I declared my # acres sovereign, that'd be a secession. I'd be laughed at and shot by the local police if I put up armed resistance, but it'd be a secession.
If a Lord left one duchy for another, it would be the same as above, though a little more murky due to the land changes. Either way, if the oath was absolved and the lands granted to the neighboring duchy by the first Duke. However, if the Lord instead changes to a Duchy that is outside the realm, then the Lord is seceding from his original realm.
The whole duchy thing in BM is one of the things I actually tend to dislike. It forces an awkward artificial feeling political structure. When you think of knights, do you think of them yelling "Halt in the name of the King!" or "Halt in the name of the Duke!"? Don't get me wrong, even historically lords high and low held considerable power. However in BM, the King just *feels* weaker than he should. That's a whole other issue, however.
Forgive the rambling. 6am. Up all night (as usual). Need sleep. Zzzzzzz