I assume it never matters if you modify it or not since you're fully allowed to fork and redistribute GPL code. It doesn't even prohibit modifications that enable compatibility with proprietary software.
The ambiguity is in whether the two programs (proprietary and GPL) together count as a "work based on the program". Your grep example seems to support the idea that they don't, and it wouldn't fall under the operating system components exemption because it "accompanies the executable". But then where is the boundary? Others have said you can't make a GPL shim to convert a library to an executable then use it in this way.
Well, in the beginning of section 2, which I quoted, a "work based on the program" is defined as a modification of the program. If you use the program as is then you do not modify it and therefore your own program is not a "work based on the program".
A GPL library is a trickier case because it's all about linking to it and potentially how that is done.
My guess is that if the shim converts the library into an executable that is usable in itself generically then you're fine (e.g. you turn some 'libgrep' into grep then uses grep). But if it only implements something like RPC through pipes specifically for use with your own program then someone might decide that this is just convoluted 'linking' and falls within the licence.
I see. It almost seems to be starting to make sense. That even brings clarity to:
"But when you distribute the same sections as part of a whole which is a work based on the Program..."
No matter how you distribute them, they never formed a "work based on the Program" anyway so the GPL doesn't spread.
If all that's correct, it seems to leave a loophole that I mentioned where you can fork the original program to make it specially compatible with your proprietary program and redistribute it under the GPL. Now when you combine them you're not modifying it because you (or your friend if need be) did that before you obtained it and the modification is none of your business.
The ambiguity is in whether the two programs (proprietary and GPL) together count as a "work based on the program". Your grep example seems to support the idea that they don't, and it wouldn't fall under the operating system components exemption because it "accompanies the executable". But then where is the boundary? Others have said you can't make a GPL shim to convert a library to an executable then use it in this way.