Well, We Belong Together: The Case for the United Kingdom by Alistair Darling, leader of the “Better Together” campaign, does contain this passage:
“The complete freedom of movement that we enjoy provides immediate opportunities for young people to have careers that span the whole of the UK. Our young people can take up jobs anywhere in the UK with no barriers or administrative difficulties On average 40,000 people a year people move back and forth across the border to take the opportunities that arise. That’s why more than 830,000 Scots are now living and working elsewhere in the UK; and why 450,000 of those happy to live and work here in Scotland were born elsewhere in the UK.”
He doesn’t explicitly say that “complete freedom of movement” will be imperilled in the event of Scottish independence, but that’s clearly what he is implying. Otherwise, why include the passage at all? It would be completely irrelevant to his argument.
I’m not sure that I’d call this “scaremongering”, though, because there is actually an issue here.
Obviously, with both in the EU, Scottish and British citizens would enjoy EU rights and freedoms in one another’s countries, but that’s not quite the same thing as the degree of freedom which currently subsists between Scotland and the other countries of the UK.
The UK and the Republic of Ireland have an agreement for a “Common Travel Area” which affords markedly greater freedom than is required simply by EU membership. An independent Scotland would be looking for something similar.
And, in principle, I’d imagine that rump-UK would be favourably disposed. But it’s not completely straightforward. The CTA works because, although the partners - the UK and the RoI - are independent and have complete freedom to set their own border and immigration policies, both set them with an eye on maintaining the practical viability of the CTA, and they do in fact consult one another extensively, if quietly, on border and immigration policies and procedures. Each country has to be willing and able to enforce the other’s policies - e.g. you’ll have difficulty getting in the the RoI if you’re a person who would not be welcome in the UK. And this is something each country has to bear in mind when setting its own policies and practices.
If Scotland becomes independent, the CTA moves from being a bilateral to being a tripartite arrangement, which means that each party has to bear in mind the immigration/border policies and practices of two other states. The possibility for tension between the conflicting demands, aspirations or interests of those other states is obvious, as is the possibility for resentment if two of the states are perceived to “gang up” on the third.
In short, what’s viable as a fairly informal bilateral arrangement may need to be a bit more structured and defined if it includes three (or more) states, with formal co-ordination of immigration policies and formal agreements over mutual enforcement. To be viable, the CTA might need to evolve into something a bit more structured and a bit more transparent; something like a mini Schengen Agreement covering Britain and Ireland. There’s no reason why that can’t happen, of course, but there’s also no inevitability about it. It’s something that the three states concerned would have to hammer out.