Gullibell
I doubt very much that the radalt initiated this warning in this instance, it was the EGPWS issuing the warning exactly as it was designed to do for the mode it was commanded to be in. An ALTITUDE ALTITUDE warning from a EGPWS must be responded to by crew avoiding action as set out in SOP. But as I said, I'm a novice on this aspect.
The "Altitude; Altitude" warning is directly triggered by the radalt. It has nothing to do with the EGPWS system.
It is triggered by descending below bugged height. If you have the radalt bug at 180' and you go below that height you get the "Altitude; Altitude" warning.
The reason it is "Altitude; Altitude" and not "Check Height" is because it uses "American English" and they don't understand the difference between height and altitude.
You state that you are a novice but you are happy to make statements that are factually incorrect and based on nothing but assumption and your limited knowledge of other aircraft systems.
PPrune at its best.