However, neither abiogenesis nor its, as far as anyone can tell, identical synonym, biopoesis, means merely "life from non-life." A key component of both (ie, the one) is "through natural processes."
Are you sure Buz understands this? He seems to think that abiogenesis and primordial soup and cosmic ooze are the same things. The only way this makes sense, is if they are all placeholders for "life from non-life."
Now, I'm perhaps over thinking this in assuming his position makes sense. But, if you ignore the word abiogenesis, and substitute in "life from non-life" then his statement is true and makes sense. Again, maybe that's not what he means, but that's how I read it.
I think that a very large part of the question is that Buz, Chuck, Portillo, and other creationists apply an entirely different definition to "evolution" than we normals do. For us, evolution is biological evolution only, the natural consequences of life doing what life naturally does. But for them, "evolution" is something entirely different, a complete atheistic worldview that demands the inclusion of abiogenesis -- the standard meaning, not your redefinitions. A large part of my position is that, if they are indeed redefining the terminology out from under us, they must at least inform us of just exactly what their definitions are. But then, that would work against their standing operating procedures of trying to generate confusion.
This is probably true, however, if they are using words incorrectly due to their own confusion, then they may not be aware that they are redefining terms. The suspiscious thing, and where I believe you are probably right, is that even after it is explained to them what the words mean, they continue to use them incorrectly. This could indicate continued confusion, as in they didn't understand the explanation given to them, or it is an act of deception.
For some reason, I tend to see Buz as just extremely confused, not purposefully deceitful. Maybe I'm wrong, maybe I'm giving him too much credit