Yer man seems to be referring to the 'basic rule is that a court must follow the precedents from a higher court, but they are not bound to follow decisions from courts lower in the hierarchy.'
So as there is no superior court to the Supreme Court in the UK they are not bound by previous decisions. They may, if it is an open question, refer the interpretation of Article 50 to the European Court.
And yes they would be able to take into account arguments that may not have been advanced in the High Court, tho' most that has been challenged since the High Court decision were grounds and matters that were commonly accepted by the parties including the Government at the Hugh Court.
They will though surely feel bound by custom, practice, precedent, and authority since the Civil War that Parliament is sovereign - not the people however a view has been expressed - and cannot be overridden by the Crown.