Another time-related concept is a beacon - that is a broadcast, unpredictable and fairly chosen random value. Eg like this weeks national lottery numbers, someone has gone to lengths to ensure they are chosen fairly, and they are published widely on TV, internet, newspapers etc. You could view the latest bitcoin block hash as a bit like a beacon. Even the miner cant control all the bits - it costs him enormous computation just to control the first 55 bits (current log2 target). There are another 101 bits he cant control; he could control 1 bit by doubling his effort and reducing his mining reward by 1/2 etc. To control them all is considered impossible.
Say each user, or users collaboratively store the sequence of beacons and vouch for the correctness. (In the case of the a time-stamp merkle hash chain, used as a beacon it helps you verify that because each block hash includes the previous hash in its preimage.)
You might wander if one could use an abstract beacon for timestamping (beacon without preimage chain). Could use a beacon to prove that you made a transaction, or mined a pool-sized mining share at a given point in time? Not fully: if you include a hash of a beacon in your mined pool share, or transaction signature, then you do prove that you did that after the beacon. However you can also back-date your operation. Eg you could intentionally include an old beacon value. Because bitcoin is more concerned about back-dating than forward dating, it doesnt help much. (Bitcoin concerns itself with first to do something, not last).
To prevent backdating, bitcoin (and time-stamp servers, and auditable name-spaces) put the hash that you are dating into the "beacon". That proves it was published then. It may also have been published earlier (ignoring validation), but at least you cant create something and then try to change its date of publication.
Unfortunately to prevent backdating seems to require transmitting all values to the timestamper/namespace manager. And in a distributed timestamper/namespace manager broadcasting to all full nodes.
A namespace manager also wants to enforce first come first served (no name reuse) so it enforces that it wont stamp names (or name hashes) that it has seen before. (If the names are random looking like public keys, hashing names is secure against brute-force, unlike hashing domain names or email addresses, so with bitcoin, like with document time-stamping you are not revealing the document/public key at the time of publication).
Adam