No.

This answer uses an out of universe information about how trail by combat works, but I think it may give some idea.

Trail by combat is a way to determine the guilt, not if the accused can walk free even if he was guilty.

Trial by combat was a method to settle accusations in the absence of witnesses or a confession in which two parties in dispute fought in single combat; the winner of the fight was proclaimed to be right. In essence, it was a judicially sanctioned duel.

If we applied this to the show, we'll see it matches.

Some examples:

• In both Tyrion's trails, no one knew for sure if he was guilty or not, so he was able to demand it.

In other cases when there was enough evidence:

• Jon executing sir Alliser: Sir Alliser couldn't because the ruler (Jon) was certain of his guilt.

• The same when Rob executed Karstark.

• The same when Ned Sentenced The mountain to death, he listened to the villager testimony and because he believed it, he passed the sentence.

Someone like The mountain can't just go around killing people then demands a trail by combat every time, as long there are witnesses, confession or a way to make the ruler certain of the guilt, he'll pass the sentence and the accused can't demand a trail by combat.

The ruler in this case was Sansa, if she witnessed the crime herself, or believed Bran, she can just pass the sentence.

No.

This answer uses an out of universe information about how trial by combat works, but I think it may give some idea.

Trial by combat is a way to determine the guilt, not if the accused can walk free even if he was guilty.

Trial by combat was a method to settle accusations in the absence of witnesses or a confession in which two parties in dispute fought in single combat; the winner of the fight was proclaimed to be right. In essence, it was a judicially sanctioned duel.

If we applied this to the show, we'll see it matches.

Some examples:

• In both Tyrion's trials, no one knew for sure if he was guilty or not, so he was able to demand it.

In other cases when there was enough evidence:

• Jon executing Ser Alliser: Ser Alliser Thorne couldn't because the ruler (Jon) was certain of his guilt.

• The same when Rob executed Rickard Karstark.

• The same when Ned sentenced The Mountain to death, he listened to the villager testimony and because he believed it, he passed the sentence.

Someone like The Mountain can't just go around killing people then demand a trial by combat every time, as long there are witnesses, confession or a way to make the ruler certain of the guilt, he'll pass the sentence and the accused can't demand a trial by combat.

The ruler in this case was Sansa, if she witnessed the crime herself, or believed Bran, she can just pass the sentence.