The example below from @ChronusZ motivates why you need to treat validators whose last validation is less than your largestIssued validation as uncommitted.
Consisder 10 nodes, 8 are honest and 2 are Byzantine. The diagrams below are the "ground truth" of the honest nodes' working ledger.
B1 (4) --- C1
/
A
\
B2 (4) --- C2