The wheel does not flex into the brakes. The wheel shifts at the top precisely because it is not flexing. When you ride, you apply force through the axle down to the contact patch; if there was flex, it would happen betwee those two force vectors, i.e. the bottom half of the wheel. The wheel would run straight acorss the top half.

Instead, what is happening is a small amount of flex at the axle, in the fork legs axle, and dropout, is allowing top of the fork or the brakes to deflect into the wheel.

This is why fork through axles are lauded, because they are oversized and stiffer.