2 men on base

[BK47]

Jurassic, what does a rule have to do with this particular play?

As you said, and the video clearly shows, Martinez was already on third base as Patterson was going back to third, however BEFORE Patterson makes it back to third he trips and falls and F2 tags him on the back (may have been the leg but I think it was the back) with the ball in his right hand. That is an out. Even you said you saw this and said that Patterson never retouchs third base. How can you have two people on the same base when it never happened? Even after Patterson got up to head back to the dugout (if you look closely and read his reaction even he thought he was out) he never touchs third base even as a precautionary measure. But that shouldnt matter as F2 had already tagged him for the out. But the umpires blew the call in my opinion and Patterson figures why not, I will try to score anyway, and they, the umpires, let the play continue. Why?

So with that, my questions still remains:

1. How is this a Righteous call?
2. Why is Martinez out?
3. Why didnt the third base coach put up more of a fight as he was there to witness the whole play? (maybe because he didnt know the rule? could be but how can the rule come into effect when still the point is there were never two people on the base at the same time)

If someone sees something that I dont please tell me but I clearly see Patterson getting tagged BEFORE he retouchs third base.