The training fee is part of the dealer invoice and from what I understand, it's to help offset training costs for MINI USA. This was introduced in the last 6 months and doesn't affect the MSRP, but it is a part of the dealer's invoice cost so it can't be taken off, just like the destination charge.
It is NOT so they can program your keyfob - there's no need to do that on 2nd gen MINIs and newer, since the user can set everything themselves. On the first gen MINIs, settings had to be programmed at the dealer, so if you wanted to change how your doors locked/unlocked, lighting, DRLs, etc. it had to be done before delivery. Now we can change everything ourselves through the settings menu on the headunit.