Actually, maybe the existence of those sequences in which black gives up a stone is EXACTLY the answer to the original question - in many cases stones that are further apart CAN be separated, but are still better than "safe" moves because they are more efficient and separating immediately is generally not good. So in addition to looking at how far you can play while still connected (which is extremely important), you should also look at how you would deal with moves that DO separate and get comfortable with the results.
The problem, of course, is that I can't think of a good example that is of appropriate difficulty. The below sequence is a well-known trick play, but does illustrate how being cut could result in a favourable outcome. Don't worry too much about the correctness of each individual move - can you tell who came out ahead?
$$Wc Initial situation - white 1 invites cut at 2
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . O . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . . , . . . |
$$ | . . 2 X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 1 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
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[go]$$Wc Initial situation - white 1 invites cut at 2
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . O . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . . , . . . |
$$ | . . 2 X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 1 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]
$$Wc 18 and a half points
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 0 . . . . . . . . . . . . . . . . |
$$ | . . . . X . O . . . . . . . . . . . . |
$$ | . 5 O 1 2 . . . . , . . . . . , . . . |
$$ | . 3 X X 7 9 . . . . . . . . . . . . . |
$$ | . 4 6 . 8 . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
- Click Here To Show Diagram Code
[go]$$Wc 18 and a half points
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 0 . . . . . . . . . . . . . . . . |
$$ | . . . . X . O . . . . . . . . . . . . |
$$ | . 5 O 1 2 . . . . , . . . . . , . . . |
$$ | . 3 X X 7 9 . . . . . . . . . . . . . |
$$ | . 4 6 . 8 . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]
$$Wc Continued
$$ ---------------------------------------
$$ | . . . . 0 . . . . . . . . . . . . . . |
$$ | . . X 6 7 8 . . . . . . . . . . . . . |
$$ | . . . 5 X 9 O . . . . . . . . . . . . |
$$ | . O O O X . . . . , . . . . . , . . . |
$$ | . O X X O O . . . . . . . . . . . . . |
$$ | 2 X X 4 X . . . . . . . . . . . . . . |
$$ | . 1 O 3 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
- Click Here To Show Diagram Code
[go]$$Wc Continued
$$ ---------------------------------------
$$ | . . . . 0 . . . . . . . . . . . . . . |
$$ | . . X 6 7 8 . . . . . . . . . . . . . |
$$ | . . . 5 X 9 O . . . . . . . . . . . . |
$$ | . O O O X . . . . , . . . . . , . . . |
$$ | . O X X O O . . . . . . . . . . . . . |
$$ | 2 X X 4 X . . . . . . . . . . . . . . |
$$ | . 1 O 3 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]
$$Wc Conclusion
$$ ---------------------------------------
$$ | . . . . X . . . . . . . . . . . . . . |
$$ | . . X X 2 X . . . . . . . . . . . . . |
$$ | . 4 6 O X O O . . . . . . . . . . . . |
$$ | 8 O O O X 1 . . . , . . . . . , . . . |
$$ | . O X X O O . . . . . . . . . . . . . |
$$ | X X X X X 5 . . . . . . . . . . . . . |
$$ | . O O O 7 3 . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
- Click Here To Show Diagram Code
[go]$$Wc Conclusion
$$ ---------------------------------------
$$ | . . . . X . . . . . . . . . . . . . . |
$$ | . . X X 2 X . . . . . . . . . . . . . |
$$ | . 4 6 O X O O . . . . . . . . . . . . |
$$ | 8 O O O X 1 . . . , . . . . . , . . . |
$$ | . O X X O O . . . . . . . . . . . . . |
$$ | X X X X X 5 . . . . . . . . . . . . . |
$$ | . O O O 7 3 . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]