I know of only one way that this can happen in windows, and has nothing to do with Steam other than their not-so-great decision to install all content into Program Files.
If you are on Windows 7 or Windows Vista, and you have UAC set to ON, then change it later to OFF, this can happen.
UAC does thing evil thing where if a program tries to write to a "protected" area like Program Files, EVEN IF YOU ARE ADMINISTRATOR, when you get a UAC prompt and give permission, it actually writes any files that would normally go into that directory into a "virtualized" directory somewhere else.
If you turn off UAC, that will no longer happen, and as an awesome bonus, it will no longer know about the files that it virtualized.
So in your case, if you had UAC on, installed a ton of games, then later got sick of UAC and turned it off, this would happen as you described.
See the second paragraph in "Features" in the article on User Account Control.
If you have done this and turn on UAC again, your content will come back, but be a TOTAL mess because if you've downloaded more stuff with UAC off, then that will be invisible when you turn UAC on, and vice versa.
this drove me a little crazy once before I realized what was happening.
i'm curious to know if this is your issue.
You cannot log onto the same Steam account in multiple places or it will kick other computers off. Additionally, I think you are unable to 'double buy' a game (though if you got the same game different ways—in a pack and a la carte, for example—you might) on the same account unless it's a gift.
However, you may be able to launch Battlefield outside of Steam (look in the steamapps
folder for the executable) however, and work from there. As you suggest, playing online with the same copy may not work, but a LAN game may. Using one copy on multiple computers simultaneously is a little grey though.
Best Answer
UPDATE
So I emailed the lead (only?) developer and got a pretty quick reply! It turns out he adds free Steam keys into the game every time he does a major patch. Below is a copy of his reply to me:
Basically what I understand is that after a patch he adds in some free keys and the first people to find them win a free copy.
According to one user it appears that at least one of the keys listed is your own.
I'm not able to confirm that directly as I bought my copy directly through Steam and did not see a key.
There is a Reddit thread, as mentioned by @ardaozkal, which seems to suggest the keys are from the beta testing.
Again I can't find any official information on this but I will keep digging.