Since it is impossible to double spend and the company is pretty trustworthy how could you determine if a transaction was sent from blockchain.info with the standard bitcoin-qt client?
When a spend transaction occurs, that transaction is relayed to peer nodes, and each peer then relays the transactions to its peers.
So when you Bitcoin-Qt/bitcoind client node receives that transaction, it most likely was several relay hops away from the sender. The transaction does not include IP information, so there's no way for your node to know any IP information except for the IP address of the node which it got the relayed transaction from.
So there is no way for your BItcoin-Qt/bitcoind client to know that the transaction was first relayed by Blockchain.info's server.
Blockchain.info itself does show that the transaction came from its own server (reported as Relayed by IP: Blockchain.info), but that's because they collect information above and beyond what is sent with the transaction.
You make an incorrect assumption though that a transaction spent using Blockchain.info/wallet is impossible to double spend. You can export the private key of a bitcoin address and use that to try a double spend race attack against the transaction. It isn't often successful, but occasionally can be successful. (A race attack can be successful perhaps one in 50 attempts, for instance, ... or greater than that or worse depending on various factors.)
