There are plenty of examples on both sides -- perhaps more from the Union than Confederates because, as you explain, the war was fought more in the Confederacy.
On the other hand, most Union armies, most of the time had reliable supply lines that Confederates could only envy.
On this subject, am reminded that -- was it Shilo? -- a Confederate route of Union forces died when advancing southern soldiers stopped to eat the mountains of rations left behind by fleeing Union troops -- and that was in a Confederate state!
Meanwhile, Confederate forces in Union states were always there, primarily or secondarily, to secure and return Union "contraband" for the Confederate war effort.
The most notorious example being JEB Stuart's ride around Gettysburg, which arguably contributed to Lee's losing the battle.
And there were others, in every Union state Confederate forces could reach.
Of course, it's true, the war's ferocity amplified as years dragged by, each new incident being worse that ones which preceded it.
Therefore, the "who started what" is unanswerable, meaning it's just as fair for me to accuse the Confederates as it is for them to accuse Union forces... right?
;-)
Quite a few southerners claimed that the southern soldiers, particularly the cavalry, were worse looters than the Union soldiers.
This no doubt varied from place to place, over time, and by commander of the unit.
But, as you say, southern forces were far more often undersupplied or even starving.