Believe it or not, but yours was the only EN thread that I could find discussing this rather surprising point.
I believe it -- it's an excellent question!

Or at least I think so, even though I really don't care much for the narrow vs broad discussion. Of course, I'm looking for discussion on the starting proficiencies from class and background. To me, the rules can only be interpreted one way, and that is for duplicate proficiencies to blow away the class restrictions, and I would like to know how this rule came about and what playtesters had against the alternative rule that if your background duplicates your choice of class skill, you simply get to remake that choice (i.e. make another choice from your class skill list) assuming all class lists contain at least five skills (so there's an actual choice involved still).
Ah, I see what you are saying. When you look at ch 1, the order for choosing things is race-class-background. That is, even though (from the character's view) the background is "prior" to the class, it is chosen after the class. That avoids your specific issue -- you've already chosen your class skills by the time you choose your background skills.
That doesn't eliminate all starting duplications, of course, but it does answer your specific concern.
Similarly, racial proficiencies are prior to class ones, which doesn't mean that you get free choice in your class skills, but that (for example) all elf rangers have Perception and three of the others from the list.
Once you've chosen them you choose a background, where the exception to the rule exists, and where there's a mechanism for substituting other skills in a custom background. So yes, in a way there is free choice, but it comes at the level of customizing backgrounds, not from class skills.
And all that falls under the "narrow" reading. The problem comes later, when (e.g.) you multi class into rogue and already have proficiency in thieves' tools. Does that grant a "free" tool proficiency? It doesn't with weapons or armours, but many (with the "broad" reading) want it to for tools.