You need to understand that neither phrase is the original (the autograph), nor the archetype but an English translation of an earlier version which will have been written itself centuries after the original first appeared.
Better, "it is not certain that either phrase is the original".
One reason why we could be looking at the original phrases is that this kind of discrepancy, where Matthew makes more sense than Mark and it's hard to see why Mark would have written as he did when writing before Matthew, occurs often. Here is another:
And having stripped Him, they put a scarlet robe around Him.
And having twisted together a crown of thorns, they put it on His head, and a reed in His right hand - Matthew 27:28,29
And they put on Him purple, and having twisted together a crown of thorns, they placed it on (literally, 'around') Him - Mark 15:17
Matthew uses the verb peritithemi (to place around) in a coherent way, Mark's use is less coherent: he says that they placed the crown of thorns around him, substituting 'him' for 'his head', thinking it meant 'on him'. Mark also uses the word 'reed' less coherently, mentioning it only when the soldiers strike Jesus with it.
It is more likely that Mark used 'place around' because he had read it in Matthew's text, than that, writing before Matthew, it came into Mark's mind some other way.
It's hard not to see a pattern of error in Mark's work that must have come about through a sort of editorial fatigue on his part.