I would venture to say that there are people out there that DO have that opinion - that if you finish with a paste/spray, the stone you finished on has a smaller impact on the final edge.
My journey so far has been to create an edge off the stone that rivals that of using a paste, but I ask 1) is that really possible, and 2) why do I care?

If pastes really are an abrasive with a finer grit level, then it makes sense that it's going to improve the edge. And if it does this, why shouldn't I use it? The only reason I don't use it is to feel the different edges off different hones in the event that a better finish before the paste will make the post-paste edge that much better, in the same way getting a good edge off 8k will set you up for an even better edge off the 12k.
So far I have only achieved a non-paste edge that rivaled a pasted edge 1 time, off my coticule.

In every case that I have received an edge from someone, either hobbyist or pro, a few laps on cBN has improved the feel of the edge for me.
As always ymmv. I have refrained from speaking my opinion on this because I'm a novice, but it has been my experience so far.