There are many weights that an aircraft can land at and a different procedure for them.

Maximum Takeoff weight (MTOW) is usually a good bit more than Maximum Landing weight. Since there is no fuel dumping capability in most aircraft, the manufacturers have developped various procedures for dealing with this.

There are graphs that depict this and it shows weight against vertical speed. So depending in how hard they land, maybe they need an inspection, maybe they don't. A fully loaded A320 does not need to burn fuel to land at any weight below MTOW.

Given the hydraulic problem and how that ties into the Airbus systems like nose whell steering, my guess is that the decision to burn fuel was to keep from starting a massive blaze if they cracked up on landing or overrun as opposed to a weight issue.