This seems to be an invention of the movie. In the book it is very clear that Quirrel cannot touch Harry:
Harry sprang toward the flame door, but Voldemort screamed "SEIZE HIM!" and the next second, Harry felt Quirrell's hand close on his wrist. At once, a needle-sharp pain seared across Harry's scar; his head felt as though it was about to split in two; he yelled, struggling with all his might, and to his surprise, Quirrell let go of him. The pain in his head lessened – he looked around wildly to see where Quirrell had gone, and saw him hunched in pain, looking at his fingers – they were blistering before his eyes.
"Seize him! SEIZE HIM!" shrieked Voldemort again. and Quirrell lunged, knocking Harry clean off his feet, landing on top of him, both hands around Harry's neck – Harry's scar was almost blinding him with pain, yet he could see Quirrell howling in agony.
"Master, I cannot hold him – my hands – my hands!"
And Quirrell, though pinning Harry to the ground with his knees, let go of his neck and stared, bewildered, at his own palms – Harry could see they looked burned, raw and shiny.
(My emphasis)
Later when Dumbledore explains what happened this is again clear:
Quirrell, full of hatred, greed, and ambition, sharing his soul with Voldemort, could not touch you for this reason. It was agony to touch a person marked by something so good."
(My emphasis)
The movie did, however, take into account the change when it provided the explanation. Instead of Dumbledore talking about how Quirrell couldn't touch Harry, he talked about how Quirrell couldn't have Harry touch him:
