Of course it matters. He was physically identified as being the person seen for a period that night by more than one witness. That was reinforced by the person offering his services as a translator. He was in the vicinity of 5a.
So, if it wasn't RM, just who was it? Another person the PJ failed to identify, interview & eliminate?
My theory is almost irrelevant to this issue.
Surely the key point is that, (at least so far as we are aware) there is nothing linking Murat to Madeleine's abduction.
Murat was legally and lawfully
entitled to be out on the night (whether he actually was or not) and there might be reasons wholly unconnected to Madeleine's disappearance why he might not be keen for it be known that he was out and about.
At most, that amount to an informal witness's obligation to answer all questions truthfully (an internal Portuguese matter, I imagine, they would not choose to pursue this far down the line.)
There was also the find of Summers and Swan that a landline phone call was made from the Murats' residence to his girlfriend at (I think) around Midnight?
Murat must have been home to make that call.