I just bought osx Mountain Lion on my MacBook Air. The apple store guy said that if you buy a software with an apple ID that someone else is using, that person can get it for free. But when I bought my Mountain Lion on my MacBook Air my mother couldn't get for free.
Yes, agreed and what I would do is make a USB key installer. CimmerianX is correct, as long as you made a purchase with your Apple ID. You can download and install to any laptop that can support the new OS X.