I actually bought MOH Tier 1 edition last week on disc at Game, it says in the corner of the box about the BF3 Beta, Im pretty sure its not a Steam game though?
Im at work at the mo so cant check, but does that mean Ive got early access too?
Brought my Tier 1 on release from retail and still no beta key. I had even attached my game to Origin months back and still nothing.
Could you maybe try activating your code on Steam and seeing if it adds a beta code also? (no idea if it would work but wouldn't do any harm)