Bjorn was standing in front of the famd Chieftain of the Sturlungar only because he wanted to kill Tyr.
But Sighvatur's earlier reaction implied that something fishy was going on here.
Bjorn did not have time for passive thoughts, all he wanted right now was Sighvatur's head, he wanted to kill so he could look for Tyr.
Tyr was clearly not here but he could see a blood-stained bed at the corner of the room.
"Bjorn Ironside, is it true your body is made of steel?" Sighvatur asked because he was curious but Bjorn did not answer him, choosing to respond instead with force.
Bjorn charged at him with intent to kill, he had every intention of killing Sighvatur and the only thing that could change his mind is if he gave him the information he sought.
Sighvatur braced himself, Sighvatur was still an unknown as he has not even shown an ounce of his true strength but Bjorn had no way of knowing this.