That's still essentially an escrow isn't it? You're at least involving as third party. I think multi-sig is probably too 'advanced' for most of the newbies in crypto as most of them seems clueless, and that's why using a trusted escrow agent might be more preferable in those situations.
Yes - the third party is an escrow agent/ arbitrator, and should probably be paid for participation. The main difference is that the escrow agent does not have to hold the funds. Also, it provides the possibility for the release of the funds if the buyer and seller both sign the transaction. In this case the escrow agent is only there in the case of a dispute.
That is how it should typically work and is a much better system if you're doing digital currency transfers.
If you're doing transfers of physical goods with bitcoin then the escrow has to hold the physical good and not the bitcoin because they have to prove the goods are what they are before they invoice the buyer.
The example explained in the OP isn't a very good one.
What should happen is, let's say Mr A is a buyer and Mr B is a seller.
Mr A deposits 4BTC worth of fiat into the escrow account. Mr B then sends a message to both of them stating the address that Mr A needs their funds to be sent to. Escrow then send an awknoledgement to both to state they have received the address/message, Mr B then sends the funds to Mr A and once the escrow sees there's enough confirmations (or wakes up if people are impatient like me and send bitcoin transactions with low fees just before they're about to fall asleep :-)) they release the fiat from their accounts to Mr B. Actually, a multisig wouldn't therefore work in this case as it would be the fiat you'd want to be escrowed as it's less traceable (not on the blockchain).
(generally an awknowledgement from a solicitor/escrow will be signed with their private key - can be a bitcoin address or a degital certificate that affirms their identity).