Essentially, he said that Sherman did not relay his position back to Washington during the campaign in an attempt to stump espionage efforts from the South. So, instead, the army acted independently from Washington, and Lincoln and his administration would actually stay up to date with Southern newspapers to find out where Sherman actually was.
He was kind of half joking when he said it, but in a "I'm oversimplifying" kind of way, not in an entirely "this is a joke" kind of way. So, does this hold any truth at all? If so, can anyone expand on how common this was done?
I think your professor hit it right on the head if you read his delivery of this topic correctly (in that what he said was more or less true, in a kind of over-simplified way). The essence of Sherman's plan was to "cut loose" from his supply trains after leaving Atlanta, and to live off the land on his way to Savannah. Grant had proven that this approach was both feasible, but also very effective at disrupting Confederate resource pools and overall morale. Grant drew up what you might call the road-map for this approach during his Vicksburg campaign, when, after more than half a dozen attempts to take the city, Grant cut loose from his base, marched south of the city, crossed the Mississippi, and marched on Vicksburg via Jackson, MS. Grant could have never gotten his wagons through that route (too much swamp and marsh), but he felt that this wouldn't matter if his army foraged liberally from the countryside and moved quickly to surround the city before Joseph Johnston could come to Pemberton's relief. Grant also saw the potential bonus of (as stated above) disrupting micro-scale southern supply depots (i.e., farms).
It's funny to note that Sherman thought Grant was crazy when he proposed this tactic during the Vicksburg campaign, yet it was Sherman who became famous for this strategy's implementation during his famed march to the sea (by then, Sherman realized the plan was indeed brilliant).
One thing you have to remember about Sherman, though: he despised the press. He assumed (sometimes correctly) that reports pertaining to his proposed movements were being leaked to the press, which then got into the hands of his Confederate foes. Sherman was vocal in his opinion that the press were glorified spies, and was paranoid about his planned advances ending up in the papers. For this reason, a central part of Sherman's strategy following his departure from Atlanta was to keep even members of his senior staff in the dark about where they were headed, and to report back to Washington as little as possible. Sherman realized that if his government and soldiers didn't know where he was going, then the enemy couldn't either.
Thus, while Sherman did keep in sporadic contact with the government during his march, overall, Washington did really have to read Confederate newspapers to get a sense of exactly where Sherman's army was. Sherman was moving fast, and was cutting so much telegraph wire that sending word back to Washington wasn't really all that feasible anyway. This was very rare during the Civil War (Lincoln was a hands-on manager, and often demanded steady streams of updates), and was only approved as a plan with Grant's urging.
[Sources - Bruce Catton, 'Grant Takes Command'; Catton, 'Glory Road'; James McPherson, 'Battle Cry of Freedom']