It's not the minimum possible, but it is the minimum typical case.
Escape velocity is the upwards velocity needed at the surface to reach an unbounded height with velocity zero. Run that in the other direction and you see an object that starts from infinity will reach Earth at escape velocity.
For that not to happen, you'd need something to perturb the object, slowing its fall or deflecting its velocity in some direction other than down. This can happen from the Moon, but it's not common given its small mass and gravitational field relative to Earth.
Escape velocity is the upwards velocity needed at the surface to reach an unbounded height with velocity zero. Run that in the other direction and you see an object that starts from infinity will reach Earth at escape velocity.
For that not to happen, you'd need something to perturb the object, slowing its fall or deflecting its velocity in some direction other than down. This can happen from the Moon, but it's not common given its small mass and gravitational field relative to Earth.