While the comic book may have played with the idea that Sabretooth could have been Logan's father (Sabretooth appears on Logan's birthdays with a surprising regularity...), the movie isn't doing so.
The second Wolverine clip indicates indeed that the teen who took the young Logan under his umbrella is actually the young Sabretooth, it seems they are actually brothers. The two have been through a lot together, but then they became at odds:
The third TV spot of Wolverine has aired on FOX Channel:
Every hero has an origin!
Wolverine is going to chop the chopper! That sounds like jumping the shark or nuking the fridge, but I' don't care: just awesome!