One way to think about my reaction to that quote is that it seems to hold the storytelling chops of their cards in rather higher esteem than is merited to claim that these are the stories the cards are telling. I'd probably have reacted better to that if it didn't seem like complimenting themselves, but you (and they) are right--it is possible to think about this more generously than I was giving it credit for. I think the cards themselves tend to cause the problems as much as they solve them, but that's the joy of a complicated, sometimes apparently conflicting set of texts which require substantial interpretation--you have the flexibility to make them mean a variety of different things, and can focus on what seems most salient in the current situation.
sidebar/ I am vaguely gob-smacked by the civility of this conversation, taken as a deviation from Internet norms. /sidebar
Some of the other rules tips (which can be found in the app under Rules->Tips and include such as "Cards don't do what they don't say" and "If it isn't called a thing, it isn't a thing") seem to focus on making sure players don't use their storytelling imaginations to make cards do more than the rules say they do. In that context, "Allow For Abstractions", along with "Cards do what they say", try to prevent players from using their storytelling imaginations to make cards say less than the rules say they do.
I agree that from a storytelling perspective the cards frequently demand improv-level "Yes, and-ing" and a strict refusal to negate their premises. As such "letting the cards tell you their stories" requires a particularly active form of listening - which to me, is one of the joys of the game when played around the tabletop. You can just play along mechanically following the rules, or you can construct a story to make it make sense, in an inevitably goofy and contorted way that would never pass muster in, say, Atlas Game's Once Upon a Time.
Also, @Pitta - assuming this does well, I think we can count on a lot more material for the app. There are currently 3 boxed sets of Pathfinder Adventure Card game out in print, with a fourth coming in October, and each set with all expansions has IIRC 33-35 scenarios total, so you're looking at something like 140 scenarios if they release everything. I like to imagine that much of the difficult work is already done before Obsidian comes along - art assets, scenario design, character balance, etc - and that as they remove the bugs from their chassis with Rise of the Runelords there should be a relatively low time cost for them to convert additional material. But then, I don't code...