If I took ten people off the street, in San Francisco itself, and asked them who made an iPhone app called "Paper" a majority would probably already tell me Facebook. Perhaps one of them would know of 53, and probably not by name. Being in the mobile software community, we know of a lot of "successful mobile apps" that are not household names. I like and use 53's Paper, but 53 is not Exxon, GE, or Facebook. My friends and family have almost certainly never heard of it. A hundred million unverified global downloads does not equal a hundred million people who remember what your poorly branded, generically named app is called. I usually think of it as "that coffee stain icon with a generic name". Honestly, 53 might do better renaming it "53". Or "Studio 53" if they wanted to skim off of another brand that probably won't fight back.
Paper by FiftyThree is a good product, but a poor choice of name, and I still can't figure out why their app icon says "53" instead of "Paper".
That said, I don't think 53 can claim any exclusive rights to the name, and I'm happy to see they haven't - they have just asked with exquisite politeness.
No. 53 needs to claim exclusivity, claim that there is no possibility of confusion, or live with the reality that if people start calling Facebook Paper just "Paper", that Facebook will legally be able to prevent 53 from using the term. With trademarks it doesn't matter who has been using it longer, only who successfully enforces it.