Erick Barkhuis:
It might well be that you're absolutely right (your explanation sounds
plausible)....but on the other hand, how has the ballpark become symbol
for such space and not any other limited space like a concert hall, a
gym, a space shuttle or a transport container?

I would guess it's simply because metaphors from baseball are so popular.
As for the meaning being what I said, see these dictionary listings:

http://www.bartleby.com/61/61/B0046100.html
http://www.merriam-webster.com/dictionary/ballpark
--
Mark Brader | "I always pass on good advice. It's the only thing
Toronto | to do with it. It is never any use to oneself."
| -- Lord Goring (Oscar Wilde: An Ideal Husband)