> If an attacker can put a random binary on your local drive then they already own your machine
Pretty much no.
>If a miscreant cuts your brake line without your knowledge,
Terrible analogy. Because it's not what's occurring here. They don't have unrestricted access to critical systems on your car. It's more like they put a brake line cutting machine in your front seat. It's not until you get into the car and say "Are you sure you want to run the program START CAR with administrative access" that your line can be cut.
Let's go back to your original idea that the machine is compromised. If I have a virus file in C:\Dont_execute_anything_from_here, is my machine compromised? No, in most cases a file sitting on the drive would not randomly self execute. But, now let's say file "bad_code.exe" was written in such a way it took over program flow from my anti-virus when it was scanned. We would certainly say that the anti-virus vendor was at fault in this case.