I have heard this argument before, and I dont agree with it. I think it fails under the fallacious thinking that since he would end up in the same place in either event, then all other things must be the same as well. The fact is, the Overland Campaign chewed up Lee's army just as much as it did the AOP. Did Grant make mistakes during the Overland Campaign? Obviously. As Gordon Rhea pointed out, one of his biggest was the ill defined command structure he had with Meade. Many of the ill fated charges were due to Meade wanting to impress Grant that he was on board with Grant's grind them down strategy. As a result Meade insisted on charges that had no chance of success in order to secure his position with Grant. That is not to let Grant off the hook, though, as the ultimate commander he had responsibility to be closer to the fighting to see the actual state of affairs, instead of deferring to Meade.Instead of the "tremendous losses" suffered by Grant in the Overland campaign, he could have just taken the major part of his force up the James and avoided those grievous losses. Or he could have eschewed the foolish frontal assaults on fortified positions, often done at the spur of the moment, and just maneuvered his way overland towards Richmond. With his overwhelming force, he had the ability to take the initiative. Instead, the AotP was a chewed-up, relatively spent force by the time it arrived at the James under Grant and needed time and reinforcements to regain its strength.
All that being said, though, by the time Lee was trapped at Petersburg he had lost most of his senior officers and almost half his army, thus forcing him into a siege that he knew could only result in one result. I think its very fallacious to assume Grant could have avoided all that fighting and end up in front of Petersburg with the exact same strategic situation.
