I would be very concerned if the Supreme Court allowed anything other than the strict rule of law to be applied when determining a case. It would be more of a constitutional crisis if the UK Supreme Court felt obliged to uphold the Courts of Session verdict because of potential political ramifications!
Quoting - slightly trimmed for clarity - from a post on another site:
"The UK Supreme Court requires that Scottish Law Lords judge on issues of Scots Law as the English Law Lords have [...] no competence on issues of Scots Law. The Cherry Case was brought under Scots Law and practice. The judgement was made on the affidavits and legal arguments brought before the Court of Session by both parties.
"The judgement can only be over-ruled by the UK Supreme Court if the Court of Session has exceeded its powers under Scots Law, in error in its interpretation of Scots Law, the evidence before it or in EU Law."
So what Supreme Court is doing is hearing arguments about whether the correct procedures - all the i dotting and t crossing was done in the right order. That the evidence submitted was submittable, that the right rigmaroles were gone through, not hearing the case all over again.
Essentially the government are hoping to 'get off on a technicality'.