I don't quite understand how someone can just claim a transaction. Does this apply to the "Strange Transactions" under Block Chain?
The short answer to your question is "yes".
You see, any transaction output has a ScriptPubKey field - a script indicating the conditions a later transaction must meet to spend that output's BTC.
In 99.999% of cases, the script just says "the spender must sign their transaction with the private key whose public key hashes to {ADDRESS}". In other words, it provides an address and requires that the spender prove that they own the address.
However, it's totally legal to require something else instead, and in a few cases, that's what someone's done, and what they've required is something I can provide, even though I don't know them or why they made a transaction like that.
I'm asking about those cases.