How is the climb gradient calculated?
Assuming that thrust is entirely in the direction of travel and the flight path angle is constant, the Lift is equal to the weight times the cosine of the flight path angle:

$L = W\cos(\gamma)$

For small $\gamma$, $\cos(\gamma) \approx 1$

E.g. for a flight path angle of 10 degrees, the error introduced by the approximation is ~ 1.5%



For unaccelerated climb, the sum of all forces in the along path direction cancel each other out:

$ T-D-W\sin(\gamma) = 0$

The gradient is $\tan (\gamma)$.

Again, for small angles, $\sin(\gamma)\approx\tan(\gamma)$

From there it is a small step to see that the calculation suggested by your colleague is acceptable for unaccelerated climbs at small flight path angles.