I agree. The consensus we now have in support of the concept and goal of UHC is unprecedented. The notion that this huge opportunity to galvanize global and national action towards (and accountability for) achieving UHC could be squandered through a technical misunderstanding seems unbelievable, but is clearly very real. It is this risk that explains why over 300 organisations and academic institutions from across the world have called on the IAEG members to review this indicator and revisit its objective - that it's not there to measure intent, but instead to measure effectiveness of financial protection measures. And it's certainly not there to dictate what type of financial protection measures a country should adopt - this would surely be at odds with the 2012 UN resolution on UHC which clearly states that the choice of a health financing system should be made within the particular context of each country.
I would add one thing.
Firstly, your point that prices are zero or at least heavily subsidized in a country's public health system overlooks a crucial and relevant point. Prices are actually rarely zero in many countries as user fees do apply and they have large scale catastrophic and impoverishing consequences. So your UK-Azerbaijan example is a good one, but in building our argument against the current indicator let's not overlook those many public systems that do have official user charges and which send millions of households into impoverishment each each.