If the puzzle is fun or really short, that's what I do too (copy/pasting is slower than reimplementing most flash puzzles).
But some puzzles, especially in the reflection category... are just long and tedious. No real thinking involved, just a bunch of tests and a lot of room for small mistakes. If I want to write the same tedious code over and over, I might as well not take breaks and keep working!
Also, we're only talking about "fastest" puzzles here, right? If you have already seen the statement of a "reverse" clash, even reimplementing it is cheating. And for golfing, what's complicated is thinking about how to reduce the code, not actually writing it, so remembering the puzzle is already an unfair advantage too.