The fundamental trick is that 4e is 2 dimensional. All of its wording uses the term "squares" rather than cubes. While there are concessions to the z-axis, it is not considered an inherent aspect of the game when dealing with, for example, character height.
As squeezing notes:
Smaller Space: A Large, Huge, or Gargantuan creature reduces its space by 1. For example, a Large creature that squeezes has a space of 1 (1 square) instead of 2 (4 squares). A Huge creature’s space changes from 3 (9 squares) to 2 (4 squares). When a Medium or smaller creature squeezes, the DM decides how narrow a space the creature can occupy. If an effect prevents a creature from leaving a square in order to squeeze, the creature cannot squeeze.
Looking at this, the "correct" answer to your question is: mu (unask the question) due to the game system not simulating that level of detail.
Functionally speaking, when the GM is designing areas, it is fair to say that small creatures don't have to squeeze, medium creatures do, and large creatures find it inaccessible. But there is seldom more granularity than creature size. Even in squeezing, there is a discussion of squares rather than cubes.
Thus, stating that a blade barrier is one square above the ground causes the system to stutter slightly as most walls have their area specified with z-axis height as a footnote. Assuming that it is the case however, it is the GM's decision to allow medium creatures to squeeze, small creatures to squeeze, or some combination of the above, reflecting the "difficulty" of squeezing under the blade barrier.