No, incorrect, Valencia still has the same duty as before, crossing the ball. He has other duties that differ as a full back to a winger, namely defensive ones, but crossing the ball is still a very important facet of his game, just as it is for most fullbacks in the modern game. If it wasn't his duty, he wouldn't be attempting loads of them in every game, it's not like he's doing it of his own will, or something. He's clearly instructed to get forward, and cross the ball. His crossing is poor, and that's why he's getting slated for it. If it was not his duty and he wasn't putting crosses in, then I'm sure nobody would care.
What you're basically saying is that because he's a fullback and not a winger now, crossing is almost irrelevant, which makes no sense, because he put more crosses in than any other player today and was used as the focal point of our crosses for the majority of the game.
The bolded part is just insane logic, though, how exactly does him being in defensive positions more have a profound effect on his ability to cross the football. Is it that when he has the ball at his feet, ready to put a cross in, he suddenly thinks "oh shit, erm, better not feck this up, what if it goes wrong and I have to run all the way back to chase the defender, oh noes, panic, ahh, hit the ankles, hit the ankles!!"