All content received is automagically re-distributed by default, correct? It is similar to BitTorrent in this regard; very different from the more common client/server paradigm.
I will have to do a bit more research to see how the default clients handle caching popular, unrequested content.
No, if you run ipfs, you only host what you choose to host and things that you have recently requested. Your node doesn't passively accept content from others to host. (Otherwise, a joker would probably saturate the entire network's hosting capacity with /dev/urandom, or everyone would saturate the network's hosting capacity with their own encrypted backups, etc.)
I think there must be something wrong with the way ipfs presents itself, because I see this misconception (that just running ipfs causes you to host anything) often.
It's likely due to people thinking that "distributed" means "distributed by default". IPFS needs to gear it's docs to make people think in terms of Bittorrent (i.e. pinning, seeding, etc) and not in terms of RAID (i.e. sharding, high availability).
Oh, I just realized I missed the word "received" in your first sentence! I don't have much to add to how you actually worded the sentence.
I think the automatic re-sharing of recently requested content is only for a short time period (elsewhere someone mentions 30 minutes). Probably not anything anyone should rely much on; it just sounds like a bonus to maybe soften the blow a little bit if you get a lot of activity suddenly.
I will have to do a bit more research to see how the default clients handle caching popular, unrequested content.