What does "'Copy Job' would like to control this computer using accessibility features" mean? Since installing OS X 10.9, I periodically get a message that

'Copy Job' would like to control this computer using accessibility features


I believe the source is SuperDuper! (2.7.1), but am unsure what it is asking for, whether to allow it, and what the consequences of denying would be.
There is a post on Dave Nanian's (the author of SuperDuper!) blog at http://www.shirt-pocket.com/blog/index.php/shadedgrey/comments/mavericks/ which explains this issue:

As you may know, our scheduling feature runs a little application called &quot;Copy Job&quot; behind the scenes...
For some reason, in Mavericks, this check (and a second one that checks whether Growl is running) now generates a scary security warning...
We've found a way around this prompt, but it requires that you delete and recreate your existing schedules...