I feel this is more a meme, rather than reality. I do check StackOverflow, but never have I took an answer verbatim.
I try to see if it's the same problem and what was the approach in deconstructing it, which I find more useful in the long run.
It depends on what you need. In most cases the code on StackOverflow is not exactly what you need, so you need to understand it in order to adapt it. But if you're looking for a specific well-defined algorithm (MD5, say) then you can just copy & paste it.
I catch people using cut and paste code all the time. If there is a spelling error in code (Especially if it is in a code comment), I can guarantee you that someone copied and pasted it from StackOverflow.