"And it really should not matter where I bought it"
I totally disagree with the above. It's imperative, let me stress EXTREMELY impertative, in this situation.
I 100% agree with this post. The fact of the matter is that a boutique is probably the most expensive option to purchase a watch--i'd imagine an authorized dealer would be more willing to discount. That being said, what you get for spending that extra cash presumably is better service, i.e. getting a free strap thrown in in the correct size (my view of the original issue. i don't see any place accepting it for an exchange) or the first look on a limited exchange piece. Maybe an invite to some of the marketing stuff that lange does (which to my knowledge is generally set up by the retailer vs. the manufacturer itself).
If you had purchased from the boutique, i would have been surprised that they wouldn't throw in that strap (if not both) for free. But for just owning a lange...with all due respect i think your expectations might have been a bit excessive. I'm speaking as a US customer and I'm fairly certain that would hold here as well as asia or wherever else.