First of all, all Union states and territories were "true", regardless of what some Confederates may have wished.
None ever voted to secede, and all supplied more troops to the Union than Confederacy.
Second, all Border States had significant slave-holding populations, but they were distinct minorities, and were unable to control either politically or militarily.
They could however challenge the majority Unionists, and did so, often with very destructive results.
In some cases these were comparable to "scorched earth" policies practiced by some Union forces at war's end.