Original post author here. Thanks -- your comment pretty much nails the answer to my question.
Edit: A problem with this is that it would be necessary for a naysayer to exhibit the other transaction (proof of double spending). But they couldn't forge such a transaction, since they don't have the private key necessary to generate the signature. So I'm still a bit puzzled by this.
Edit 2: And it appears that bcoates is making the same point.
Btw, Ripple is basically a two-phase commit protocol. The problem is trust - ripple has basically decided to trust a centralized list of nodes, whereas bitcoin does not require this trust.
The problem is network disruption. Your system would work if you could guarantee all nodes in the network could communicate with each other every 10 minutes. What happens if this is not possible?
This scenario is called a netsplit in Bitcoin parlance. It has happened before, and it will happen again. In bitcoin, healing a netsplit is relatively easy, you pick the longest chain and you allow all the transactions from the smaller chains to be re-added to blocks in the new official chain.
In your system, if you had a double-spend where both sides ended up being accepted due to a netsplit, which one would win during the healing process? In bitcoin, the winner is the one that happens to be in the longest chain.
Secondly, how would you store the infocoin ledger in your system? The advantage of the bitcoin blockchain is that it provides an official source for all transactions that is easy to verify. A new node can come in, download the block chain and be certain they have all the information available about bitcoin ownership, with no holes. In your system, without a blockchain, how do you guarantee you have a record of all transactions, with no gaps?
"In your system, if you had a double-spend where both sides ended up being accepted due to a netsplit, which one would win during the healing process? In bitcoin, the winner is the one that happens to be in the longest chain."
That doesn't seem to be unanswerable, and it's not like "happens to be on the longest chain" is more deserving or anything, it just happens to be the way it works in bitcoin.
Edit: A problem with this is that it would be necessary for a naysayer to exhibit the other transaction (proof of double spending). But they couldn't forge such a transaction, since they don't have the private key necessary to generate the signature. So I'm still a bit puzzled by this.
Edit 2: And it appears that bcoates is making the same point.