The "max all up weight" in the definition is wrong.
If you check the Flight Test Guide for FAR 25 (AC25-7A) it says:
To determine VMCA, use the configuration specified in § 25.149, except that VMCA is normally determined at minimum weight in order to minimize the stall speed and because static VMCA decreases with increased weight if a 5-degree bank angle is used.
Additionally, the same document states (in the introduction to the minimum control speed section:
Explanation. Section 25.149 defines requirements for minimum control speeds during takeoff climb (VMC), during takeoff ground roll (VMCG), and during approach and landing (VMCL and VMCL-2). The VMC (commonly referred to as VMCA) requirements are specified in §§ 25.149(a), (b), (c) and (d); the VMCG requirements are described in § 25.149(e); and the VMCL and VMCL-2 requirements are covered in §§ 25.149(f), (g) and (h).
(Those are on about page 91 of the copy I have, by the way)
VMC and VMCA are used interchangeably in the FAR 25 world.