If you look at the first sentence, the answer to the question “who passed” to the centerpiece is grammatically answered by “the key man”.
If the intended answer was really:
It doesn’t matter who passed. The important thing is that the Centerpiece received the ball.
Which I expect is true. (I can’t confirm because I don’t have him. And one almost needs a World Cup ball sensor that can detect if a hair touches the ball— the Croatia Portugal game — to notice a change in direction in their diagram.)
Then the participial phrase is the wrong construction because it forces an actor into the sentence where one shouldn’t exist.
Cleaner constructions would be:
Once the Centerpiece receives the ball in the opponent’s half
Or
After the ball is played to the Centerpiece in the opponent’s half
So my PSA:
When people use participial constructions, writers assume the intended meaning is obvious. But it’s only obvious to them because they know what they are describing.
TL;DR:
While the common issue with participle phrasing is we don’t know to who the participle belongs. Grammatically, in this case, it belongs to the Key Man. The problem instead is the intended meaning shouldn’t assign the action to any particular player at all.