You are right, between multi-classing and backgrounds (which don't train you but can give access), there are few if any reasons to choose skill training. This is taken from few to less then zero with bards, as it is almost always a better option to simply take "Bard of All Trades" (Dragon Magazine #383). +4 to all untrained skills is almost always better than +5 to one.
It is important to note, however, that all multi-classing feats have requirements that the player has to meet. It's not always as easy as you'd think to find a multi-class feat that you qualify for and also offers the skill you want. This will often leave a player with a difficult RP'ing decision, making Skill Training appear more attractive.