BBC scotland has 10% of the viewing population but doesn't get anywhere close to 10% of the funding. (Last time I checked it was less than 7%)
What should happen is BBC should be advert driven in Scotland to make up any shortfall. People in Scotland will still be able to get the UK channels via Freeview and satellite same as Rep Ireland viewers can.
It's a trivial point.
Also new nations would have quite a bit of support from international bodies.
But you're making the typical false assumption of the "we don't get our fair share campaign".
You're assuming that because only about 7% of the funding is spent directly on Scottish content that's it.
It's not, as a lot of the most popular content in Scotland is from other regions...(and very little of the Scottish specific content has any value outside of Scotland)
Let alone the behind the scenes things that have their true cost for a region hidden because it's used generally across the organisation and thus the money comes from the central pot (even if it's used locally).
If it's such a trivial point then why is it brought up at all, and why is it so hard for the white paper to realise that there would be rights issues*.
This is a great example of how the "yes campaign" aren't thinking things through.
It's not up to the BBC to decide what they can let people outside the BBC's viewing area see - it's up to the rights holders, and they tend to like to sell those rights separately by country, or get additional payments.
IIRC in the case of the republic of Ireland there is some form of agreement that has been negotiated with the content providers and some payments.
The same sort of faulty arguments are all over the place with the Scottish independence campaign, as it's usually really quite hard to see how much is spent in any one region out of funding that might be from a general purpose pot, rather than specifically earmarked.
For example the current Diplomatic missions and Embassies we have in various countries will all be funded by Westminister, and Scots will get full use of them, but the cost is never seen as a "Scottish cost" in the accounting the SNP etc like to use.
Likewise I suspect the cost of search and rescue in the waters around Scotland won't be from a pot specifically earmarked as "Scottish", but as a part of the S&R budget generally.
The same is true of all sorts of things (another example is things like the cost of the DVLA etc).
*Rights issues that could mean that apart from regions where they receive from an English transmitter, once they go independent they could lose freeview versions of current UK channels - I suspect that all the current contracts will be for the UK, and that from a legal point of view could be quite tricky if Scotland became independent and no longer part of the UK (if a legal document in a rights case refers to the UK, parts of the UK that break off are likely to no longer be covered - and even if they are it could take years of court cases to sort out all the thousands of contract.)...