"Equivalent" means "equal in value, function, meaning" and they are not, as DannoB's incorrect definition is a simplified one with a narrow application to certain types of photography. It is arguably useful to beginners like DannoB, but the same argument can be made that the exposure triangle is useful to beginners. I do not think it is as the exposure triangle incorrectly teaches that ISO is part of exposure.
I think it is better to educate beginners properly rather than improperly.
As to the concept of equivalence, assuming you mean photographic equivalence, I generally agree with it. However this thread is not about equivalence and I agree with Danno that threads should not be hijacked even by the site owner. This thread is about noisy photos which is a function of exposure but not a function of equivalence as used in this context.