wheel - 10:11 pm on Feb 7, 2011 (gmt 0)
MAMP has nothing to do with the problem you were having. It's a DNS issue. Your computer was looking for example.com. The general order of finding out where a site is located is:
your local hosts file
Since your local hosts file is normally mostly blank, it looks, sees nothing, then queries the web to find a site. You're simply inserting an address for example.com, overriding the normal query that everyone else does.
MAMP and MAMP pro then either serve the page or they don't. But you've already established that they were serving the pages just fine.
Play with the hosts file a bit. It's handy for stuff like you're doing. You can speed up queries, i.e I have my mail server IP address in mine, so when I check email I don't have to ask on the web every time as to where my email server is - it grabs it from my hosts file.
If you have a static IP on your PC, and your router redirects http requests to your desktop, then you can screw with your client's hosts file and point their website to your IP. Then they can watch the development of the new site on your PC as well. (this is similiar to what is done when developing on a new/second webserver. Change your hosts file to the new IP and you automatically go to the new webserver. Everyone else still sees the old one. At end of development, change the DNS and that moves everyone else over to the new server).