Lee was correct. He knew what getting bottled up would lead to and it ultimately happened.
We know, sitting here 160+ years after the fact, what Grant did to Lee once the war became static. Once both sides settled on Petersburg as the place, Grant eventually cut every supply line and destroyed all the surrounding transportation infrastructure Lee could use. This came at great cost and required coordinated actions far away from Lee's control in the Shenandoah Valley, eastern North Carolina, and on a smaller scale the raids from east Tennessee into southwest Virginia/west to central North Carolina. Even Sherman moving from Georgia through the Carolinas had the possible end goal of helping destroy Lee if necessary. Lee's army was starved and demoralized deserters melted away by Grant's design. The remnants had nowhere worthwhile to go, no Confederate nation left to defend, so Lee surrendered.
Lee only held out as long as he did because things like interior lines, terrain and field works. But those things aren't everything. Grant repeatedly and deliberately threw blow after blow at Lee and met a stubborn defense from his opponent each time. But he also destroyed Lee's ability to make war and killed the desire to make more war from the lowly deserting privates up to Lee himself in the end when he finally gave up.