Not true. Well, it is a bit complicated, but it is not true in the way that it sounds.
Scotland has a separate legal system to England-and-Wales (as also does Northern Ireland) and the Scottish courts are largely independent of the English ones - though I think some appeals can still go to the Judicial Committee of the Privy Council.
But Scotland's statute law, except for devolved matters - and then only by convention, is largely the same as England's, and Westminster *can* legislate for anything within Scotland but will generally not do so for devolved matters without the Scottish Parliament's consent.
The possible sticking point is this: it appears that any exit from the EU will require the consent of the Scottish Parliament as a result of the Scotland Act (this is not exactly clear cut, but the consensus is that it will). If as is expected Scotland vote clearly to Remain then a price would be exacted for this consent, whether in the way of guarantees for Scotland or a further referendum or support in negotiating for Scotland to remain in the EU. It's a matter of political clout what happens after that.