. . . [T]he central question raised in the suit - whether extended residence on free soil liberated a slave - was not an issue in American politics and had already been tested many times in the Missouri courts, with consistent results. . . . Once the subject of a suit for freedom was raised, anyone familiar with Missouri law could have told the Scotts that they had a very strong case. Again and again, the highest court of the state had ruled that a master who took his slave to reside in a state or territory where slavery was prohibited thereby emancipated him.
The Dred Scott Case, pages 251 & 252.
Since it was Missouri law that was cited in the suit and not Illinois law it appears to me that the full faith and credit clause is not in play.
My understanding is Missouri was a slave state, where Scott lived. His owner took him on brief visits to Illinois, a non-slave state. From what I can tell, there was no "extended residence" in Illinois or a territory, so I'm not sure this passage applies to this case.
Despite Taney's somewhat convoluted reasoning, I don't see how the slave-owner's property, Scott, could be taken from him justifiably by operation of law because of Scott's brief presence in Illinois.
State courts are not the highest authority. A state law in conflict with a Constitutional law will be struck down by the Federal Courts, and that is what essentially occurred with the Dred Scott Decision.