I'm sorry, but that is completely wrong from beginging to end!
And forgive my use of both bold and underline, but it was so wrong it needed it!

Firstly, the Schengen area is a free movemenet (of PEOPLE) area, where people can move about within without expecting to encounter imigration controls normally. [Controls can be reintroduced or applied in special circumstances]

Next we have the Euro zone, this is simply countries using the Euro as their currency.

Next we have the European common customs and VAT area, this covers places that charge VAT (sales taxes), and levy customs duties, within a specified range - i.e. only moderate deviation from each other.
Consumers can move goods between places and order items for other places within this area and they will not be subject to any customs duty or import sales taxes.

We also have, although you don't really mention, the European Union, this is a political union of countries which is beyond the scope of this post. [Further there is also the European Economic Area. Futher....]

But the key point is that NONE of these areas overlap exactly, nor do any fit inside each other.

Let us know remove the word schengen from this discussion. As I said, this is about movement of people and encountering imgration controls. There are countries (e.g. switzerland with the Swiss franc) that are part of schengen but don't use the euro, not part of the schengen zone.
[There are plenty of other exceptions against different criteria, but the swiss franc ought to demonstrate the concept of how this has no relevance.]

The key area for Vat reclaims, is the European common customs and VAT area.

Now, currency has no relation to this. The United Kingdom (using the pound) is inside it. And other places such as the canary islands (part of the country of Spain, and using the Euro) are outside. Also outside the common customs and VAT area are places such as Gibraltar (using the pound, though not part of the UK). However, Gibraltar, the canary islands and other places outside the VAT area are fully part of the EU and EEA, etc.

So, and sorry if this seems rambly, there are places OUTSIDE the common customs and VAT area (including parts of other countries and other european countries and members of the EU) using the same currencies as places inside the VAT area, and there is no problem obtaining VAT refunds in the same currency.

Sadly I don't have a venn diagram to hand, but I just wanted to get across how wrong the arguments in your post were.

N.b. I note fully, that you were raising it as a possiblity and did not know if you were correct. It is easy to get confused and apply a very simple model to things when you don't know the intricacies.