UNITED STATES STANDARD FOR
REQUIRED NAVIGATION PERFORMANCE
(RNP) APPROACH PROCEDURES WITH
SPECIAL AIRCRAFT AND AIRCREW
AUTHORIZATION REQUIRED (SAAAR)
1.4.13 Height Above Touchdown (HAT).
The HAT is the height of the DA above the highest point in the first 3,000 ft of the landing runway (touchdown zone elevation). See figure 1-5
This is the official wording and therefore the definition. If your company wants to add to its SOPS, as it sees fit, then it should find its own term to describe its own standard. These things are there for a purpose and should not be confused. If you haven't done so already, show him the above document.