Your explanation makes sense, but it isn't correct. Based on the number of times I've had this conversation, I'd say there is massive misunderstanding around the word "closure" in the Perl community.

Here's a definition of closure from Damian Conway:

"In Perl, a closure is just a subroutine that refers to one or more lexical variables declared outside the subroutine itself" - OO perl, p 56.

I grabbed that quote from a post on the Perl6 list, but I've used that as my standard definition of closure ever since the book came out. It's really the only one I've seen that makes sense.

Note that merlyn also agrees with me, as shown here in this post to the mod_perl list.