The analogy isn't quite right though is it? It's more like you owning the lease to a shop and then you not your neighbour running the business from it. In that case it may be said that they are link because the one exists to facilitate the business of the other. The same applies to the Virgin example, common branding etc doesn't mean they are linked if they are carrying out different business but if one existed solely to facilitate another they may.
...but you're absolutely right these are the fine points of law and the situation can revolve around a single word somewhere on a piece of paper. The example you've given with your interpretation and the alternative I've offered apply demonstrates how you can have two parties look at the same situation, for them to have different views and for both to be absolutely sure that they are right. That's exactly why it takes a judge to resolve such things and why it can be so unclear and take so long with all documentation, legal arguments ect to be examined.
Simply means non of us can say anything for certain until there,s a judgement and even then it's usual open to appeal.
In terms of your example the argument going on at the moment is "is the you who owes the lease legally different to the you running the business or are they really one in the same?", it's enough to give you an identify crisis which in effect is exactly what this is!