You guys are making this more complicated than it has to be.
-Join an invite only session
-Buy any car you want from the internet (You'll need to have enough to buy the vehicle)
-Wait until you get the 2nd text message saying it's in your garage
-Leave GTA Online (Pause menu->Online->Leave GTA Online)
-Join another invite only session
Your new car will be in the garage and the money spent on it will be back in your bank. This also works for car mods. Go into LSC, buy all the mods you want, exit LSC, leave GTA online, rejoin invite only session.
Also, the above steps I listed isn't a glitch. It's due to the cloud servers being screwed up at the moment.
Any chance this works with buying helicopters, planes, military hardware and other special vehicles?
Yes. Confirmed working for those things, also apartments, wait until you get the text from Pegasus saying your vehicle is ready to be used. Does not work with guns, ammo, clothing.
edit: if your worried try buying a cheap motorcycle or that jetski at first to make sure it works for you.