My guess is that the expert is referring to the slight change in angle, and possibly your position, while you recompose. If it helps understand their issue, and why it probably does not matter, some rambling...
A lens has a plane of focus. So if you take a picture of a wall that you are facing, and you are perfectly square to the wall, let's say that the entire image is in good focus. That means that your lens has a flat focal plane. Now holding that image in your mind, mentally measure the distance to the very center of the frame, and then to the very edge of the frame at the wall.
The center is of course closer than the edge (further by the inverse cosin of the angle of the lens if your trig is fresh). The wider the lens angle, the further it is (imagine a fish eye on a wide wall, it could be MUCH further).
So in a simple case, now imagine that you focused on that spot on the wall closest to you (the center), remove your thumb from the AF, and turn left until that point is at the very edge. The distance to the point stayed the same, but you are now on a part of the lens that was in focus at a longer distance. Presto -- back focus.
I suspect that kind of scenario is what your expert was trying to describe.
Now in reality focal planes may not be flat, so how pronounced this is varies by lens. But more to the point it varies by distance, fstop and focal length.
To put this into perspective, consider a 200mm lens on an FX body at 100' distance and assume it has a flat field of focus. You have a field of view of about 12.5 degrees, which will give you an image about 22' wide. The difference in distance between from the camera to the edge of that image, compared to the center, is about .6', while the DOF at F2.8 at the same distance is 12'. In other words it cannot make a difference at that distance, your DOF is far, far larger than the focus shift by shifting the view.
Now consider an 85mm/F1.4 portrait taken at 6' (field of view 28.5 degrees). The depth of field is only .12' now, but for the same shift of angle the distance variation is about .2' or almost twice my depth of field (really more like 3-4x since my focus point would be at the center of the DOF). So if I focus on the eyes in the center, and shift them off to the edge, they are now out of focus (if the focal plane is flat).
Focal planes are not perfectly flat, and so exactly how much this impact has varies by lens. The longer the lens, the further the working distance, and the higher (slower) the F-stop, the less it matters. So for longer lenses, greater distances and higher fstops, it never matters. If your events are sports, that probably means you could never detect the difference.
Shooting up close with wide angles or very fast lenses, and I would take more caution in using that technique.
But I think that's the substance of what they guy was trying to convey.
Incidentally, one other consideration that says you are doing well, is that the accuracy of some of the outer AF sensors is always worse than the center. So for most subjects where the DOF is fine, using the center is a good way of getting better focus than the outside may do.