I don't think we can solve this by scrabbling around among the verbiage. There is nothing clear cut so we are picking our preferred inferences.
Both 'catch' and 'pick-up' requires the player to make an immediate 'hold' on the ball in the FoP to arrest any movement before play is allowed to continue.
So, if Blue, who happens to be spread-eagled on the ground with a foot in touch, reaches out and grounds a ball last played by Red, shouldn't the call be a Red LO if the ball was static, Blue LO if the ball was still rolling?
And if Blue should knock the ball direct into touch or back into his arms (in effect, touch), a PK?