A customer would like to lease an IP address and point it to a dedicated web server with the intention of "masking" the server's IP address so it would be difficult to tell where the site is hosted.

I found a company that leases IP addresses here: http://www.webhostingtalk.com/showthread.php?t=1191688

Is this even possible? Can they rent an IP address from a 3rd party in order to hide the server's IP address?

Update:

My client will be hosting a government leaks site and is trying to become Raid-Proof similar to what the pirate bay did: http://torrentfreak.com/pirate-bay-moves-to-the-cloud-becomes-raid-proof-121017/

Only that I'm worried about using a reverse proxy because of the latency it could cause having the app servers hosted in one data center and the load balancer/reverse proxy in other and also having to pay twice for bandwidth.